{"id":128340,"date":"2021-09-16T14:51:22","date_gmt":"2021-09-16T09:21:22","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=128340"},"modified":"2021-09-16T14:51:27","modified_gmt":"2021-09-16T09:21:27","slug":"rd-sharma-class-10-solutions-chapter-14-exercise-14-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-3\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.3 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-128398\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.3.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.3.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-14-Exercise-14.3-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3:\u00a0<\/strong>The majority of the problems in this exercise are based on section formulae. The <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Class 10 Solutions<\/strong><\/a> is an excellent resource for learning how to solve such problems correctly. Students can also use the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-co-ordinate-geometry\/\"><strong>RD Sharma Solutions for Class 10 Maths Chapter 14 Co-ordinate Geometry<\/strong><\/a> Exercise 14.3 PDF, to gain confidence in solving this exercise.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d7e14ea7d46\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" 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class=\"ez-toc-section\" id=\"download-rd-sharma-class-10-solutions-chapter-14-exercise-143-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-14-Exercise-14.3.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-14-Exercise-14.3.pdf\">RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-14-exercise-143-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 14 Exercise 14.3- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 1.<br \/>Find the coordinates of the point which divides the line segment joining (-1, 3) and (4, -7) internally in the ratio 3 : 4.<br \/>Solution:<br \/>The line segment joining the points A (-1,3) and B (4, -7) is divided into the ratio 3 : 4<br \/>Let P (x, y) divides AB in the ratio 3 : 4<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1748\/42010889084_07d150e8f8_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry \" width=\"321\" height=\"117\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1736\/42010888924_b29aabcb99_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma \" width=\"308\" height=\"242\" \/><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 2.<br \/>Find the points of trisection of the line segment joining the points :<br \/>(i) (5, -6) and (-7, 5)<br \/>(ii) (3, -2) and (-3, -4)<br \/>(iii) (2, -2) and (-7, 4) [NCERT]<br \/>Solution:<br \/>(i) The line segment whose end points are A (5, -6) and B (-7,5) which is trisected at C and D<br \/>C divides it in the ratio 1 : 2<br \/>i.e., AC : CB = 1 : 2<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1750\/42010889974_ee118ef48b_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry \" width=\"329\" height=\"479\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1757\/42010889274_e91177329f_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma \" width=\"363\" height=\"555\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/42010889504_b9cd18cd14_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry \" width=\"362\" height=\"422\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1755\/42010889704_960dcfcc2d_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma \" width=\"346\" height=\"185\" \/><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 3.<br \/>Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0) (4,3) and (1, 2) meet.<br \/>Solution:<br \/>Let the vertices of the parallelogram ABCD be A (-2, -1), B (1, 0), C (4, 3) and D (1, 2) in which AC and BD are its diagonals which bisect each other at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/42010890484_1a78120904_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry \" width=\"337\" height=\"366\" \/><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 4.<br \/>Prove that the points (3, -2), (4, 0), (6, -3) and (5, -5) are the vertices of a parallelogram.<br \/>Solution:<br \/>Let the vertices of the quadrilateral ABCD be A (3, -2), B (4, 0), C (6, -3) and D (5, -5)<br \/>Now co-ordinates of the mid-point of AC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/42010891154_4d2ddb85ed_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry \" width=\"226\" height=\"66\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/42010890814_651d8e4288_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry \" width=\"336\" height=\"200\" \/><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 5.<br \/>If P (9a \u2013 2, -b) divides the line segment joining A (3a + 1, -3) and B (8a, 5) in the ratio 3 : 1, find the values of a and b. [NCERT Exemplar]<br \/>Solution:<br \/>Let P (9a \u2013 2, -b) divides AB internally in the ratio 3 : 1.<br \/>By section formula,<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1754\/42010891384_7ed31139b6_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 14 Co-Ordinate Geometry \" width=\"354\" height=\"589\" \/><br \/>=&gt; 9a \u2013 9 = 0<br \/>a = 1<\/p>\n<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Question 6.<br \/>If (a, b) is the mid-point of the line segment joining the points A (10, -6), B (k, 4) and a \u2013 2b = 18, find the value of k and the distance AB. [NCERT Exemplar]<br \/>Solution:<br \/>Since, (a, b) is the mid-point of line segment AB.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1748\/42010891904_14389e6447_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 14 Co-Ordinate Geometry \" width=\"360\" height=\"469\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/42010891534_6234372db5_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 14 Co-Ordinate Geometry \" width=\"353\" height=\"209\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1721\/42010891694_c79c99b5e0_o.png\" alt=\"Learncbse.In Class 10 Chapter 14 Co-Ordinate Geometry \" width=\"330\" height=\"229\" \/><\/p>\n<p>Question 7.<br \/>Find the ratio in which the points (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7). Also, find the value of y. (C.B.S.E. 2009)<br \/>Solution:<br \/>Let the point P (2, y) divides the line segment joining the points A (-2, 2) and B (3, 7) in the ratio m<sub>1<\/sub>\u00a0: m<sub>2<\/sub><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1757\/42010892134_4b9fa38d6c_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 14 Co-Ordinate Geometry \" width=\"330\" height=\"328\" \/><\/p>\n<p>Question 8.<br \/>If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.<br \/>Solution:<br \/>In \u2206ABC, the vertices are A (-1, 3), B (1, -1) and C (5, 1)<br \/>D is the mid-point of BC<br \/>Co-ordinates of D will be (1+52\u00a0,\u00a0\u22121+12)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/42010892634_f91de9834c_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"340\" height=\"409\" \/><\/p>\n<p>Question 9.<br \/>If the points P, Q (x, 7), R, S (6, y) in this order divide the line segment joining A (2, p) and B (7,10) in 5 equal parts, find x, y and p. [CBSE 2015]<br \/>Solution:<br \/>Points P, Q (x, 7), R, S (6, y) in order divides a line segment joining A (2, p) and B (7, 10) in 5 equal parts<br \/>i.e., AP = PQ = QR = RS = SB<br \/>Q is the mid point of A and S<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/42010892984_4958464275_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 14 Co-Ordinate Geometry\" width=\"349\" height=\"272\" \/><\/p>\n<p>Question 10.<br \/>If a vertex of a triangle be (1, 1) and the middle points of the sides through it be (-2, 3) and (5, 2), find the other vertices.<br \/>Solution:<br \/>Let co-ordinates of one vertex A are (1, 1) and mid-points of AB and AC are D (-2, 3) and E (5, 2)<br \/>Let the co-ordinates of B be (x<sub>1<\/sub>, y<sub>1<\/sub>) and C be (x<sub>2<\/sub>, y<sub>2<\/sub>)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1722\/42010893734_414d686e80_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"344\" height=\"534\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1728\/42010893254_b21b88828b_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 14 Co-Ordinate Geometry \" width=\"259\" height=\"187\" \/><\/p>\n<p>Question 11.<br \/>(i) In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis ? Also find the co-ordinates of the point of division. [CBSE 2006C]<br \/>(ii) In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5,\u00a0\u2212215) ?<br \/>Solution:<br \/>(i) The point lies on y-axis<br \/>Its abscissa is O<br \/>Let the point (0, y) intersects the line joining the points (-2, -3) and (3, 7) in the ratio m : n<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1725\/42010894324_26ccc4cb65_o.png\" alt=\"Class 10 RD Sharma Chapter 14 Co-Ordinate Geometry\" width=\"338\" height=\"354\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1741\/42010893964_99b81d2e68_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"363\" height=\"370\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1731\/40918348440_23ee9e0e88_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 14 Co-Ordinate Geometry\" width=\"209\" height=\"115\" \/><\/p>\n<p>Question 12.<br \/>If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0, find the value of k.<br \/>Solution:<br \/>Mid-point of the line joining the points (3, 4) and (k, 7) is (x, y)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1745\/42010894544_7590719f92_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"281\" height=\"259\" \/><\/p>\n<p>Question 13.<br \/>Find the ratio in which the points P (34\u00a0,\u00a0512) divides the line segments joining the points A (12\u00a0,\u00a032) and B (2, -5). [CBSE 2015]<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1751\/42010895244_7c69a9a431_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 14 Co-Ordinate Geometry\" width=\"354\" height=\"346\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1746\/42010894694_e25c3a875d_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 14 Co-Ordinate Geometry\" width=\"203\" height=\"82\" \/><\/p>\n<p>Question 14.<br \/>Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by (i) x-axis (ii) y-axis. Also, find the co-ordinates of the point of division in each case.<br \/>Solution:<br \/>(i) Ordinate of a point on x-axis is zero<br \/>Let the co-ordinate of the point on x-axis be (0, x)<br \/>But (x, 0) is a point which divides the line segment joining the points (-2, -3) and (5, 6) in the ratio m : n<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1728\/42010895734_b9c671816a_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"315\" height=\"331\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1745\/42010895354_1cab80d64b_o.png\" alt=\"RD Sharma 10 Chapter 14 Co-Ordinate Geometry\" width=\"357\" height=\"303\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1745\/28855237178_23b5e90e30_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"333\" height=\"127\" \/><\/p>\n<p>Question 15.<br \/>Prove that the points (4, 5), (7, 6), (6, 3), (3, 2) are the vertices of a parallelogram. Is it a rectangle ?<br \/>Solution:<br \/>The vertices of a parallelogram ABCD are A (4, 5), B (7, 6), C (6, 3), and D (3, 2)<br \/>The diagonals AC and BD bisect each other at O<br \/>O is the mid-point of AC as well as of BD<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1746\/42010896414_8f1a43ea80_o.png\" alt=\"RD Sharma 10 Chapter 14 Co-Ordinate Geometry\" width=\"353\" height=\"450\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1759\/42010895904_49d2789ac4_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry \" width=\"343\" height=\"189\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1758\/42010896074_e8e1364055_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"320\" height=\"179\" \/><\/p>\n<p>Question 16.<br \/>Prove that (4, 3), (6, 4), (5, 6) and (3, 5) are the angular points of a square.<br \/>Solution:<br \/>Let A (4, 3), B (6, 4), C (5, 6) and D (3, 5) are the vertices of a square ABCD.<br \/>AC and BD are its diagonals which bisects each other at O.<br \/>O is the mid-point of AC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/28855238248_867ac18d54_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"349\" height=\"598\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1753\/28855237958_1a055a393b_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"327\" height=\"315\" \/><br \/>The diagonals of the quadrilateral ABCD are equal and bisect eachother at O and sides are equal<br \/>ABCD is a square<\/p>\n<p>Question 17.<br \/>Prove that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices of a rectangle.<br \/>Solution:<br \/>Let the vertices of a quadrilateral ABCD are A (-4, -1), B (-2, -4), C (4, 0) and D (2, 3)<br \/>Join AC and BD which intersect eachother at O<br \/>If O is the mid-point of AC then its co<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1760\/28855238678_91e8ba125a_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"361\" height=\"374\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1734\/28855238458_be6d718eff_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"355\" height=\"395\" \/><\/p>\n<p>Question 18.<br \/>Find the lengths of the medians of a triangle whose vertices are A (-1, 3), B (1, -1) and C (5, 1).<br \/>Solution:<br \/>The co-ordinates of the vertices of \u2206ABC are A (-1, 3), B (1, -1) and C (5, 1)<br \/>D, E and F are the mid-points of sides BC, CA and AB respectively<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1724\/28855239188_2f8f4917c3_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"302\" height=\"389\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1725\/28855238928_41e001ec95_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 14 Co-Ordinate Geometry\" width=\"323\" height=\"502\" \/><\/p>\n<p>Question 19.<br \/>Find the ratio in which the line segment joining the pionts A (3, -3) and B (-2, 7) is divided by x-axis. Also, find the coordinates of the point of division. [CBSE 2014]<br \/>Solution:<br \/>Let a point P (x, 0)<br \/>x-axis divides the line segment joining the points A (3, -3) and B (-2, 7) in the ratio m<sub>1<\/sub>\u00a0: m<sub>2<\/sub><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/28855239728_d02c3acfbc_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"245\" height=\"244\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/28855239508_253f52c7fa_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"312\" height=\"234\" \/><\/p>\n<p>Question 20.<br \/>Find the ratio in which the point P (x, 2) divides the line segment joining the points A (12, 5) and B (4, -3). Also, find the value of x. [CBSE 2014]<br \/>Solution:<br \/>Let P (x, 2) divides the line segment joining the points A (12, 5) and B (4, -3) in the ratio m<sub>1<\/sub>\u00a0: m<sub>2<\/sub><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1760\/28855239958_aa0a64c59b_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 14 Co-Ordinate Geometry\" width=\"310\" height=\"480\" \/><\/p>\n<p>Question 21.<br \/>Find the ratio in which the point P (-1, y) lying on the line segment joining A (-3, 10) and B (6, -8) divides it. Also find the value of y.<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1756\/40918353930_174c2740a6_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry \" width=\"336\" height=\"544\" \/><\/p>\n<p>Question 22.<br \/>Find the coordinates of a point A, where AB is a diameter of the circle whose centre is (2, -3) and B is (1, 4).<br \/>Solution:<br \/>AB is the diameter of the circle and O is the centre of the circle<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1722\/40918354740_544b801704_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"290\" height=\"236\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1759\/40918354450_d1a919967e_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"327\" height=\"143\" \/><\/p>\n<p>Question 23.<br \/>If the points (-2, -1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.<br \/>Solution:<br \/>In ||gm ABCD, co-ordinates of A (-2, -1), B (1, 0),C(x, 3) and D(1, y)<br \/>AC and BD are its diagonals which bisect eachother at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/40918355150_c9804254f7_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"357\" height=\"573\" \/><br \/>x = 4, y = 2<\/p>\n<p>Question 24.<br \/>The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.<br \/>Solution:<br \/>The co-ordinates of vertices of a quadrilateral ABCD are A (2,0), B (9,1), C (11,6) and D (4, 4)<br \/>AC and BD are its diagonals which intersect eachother at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1758\/40918355490_2e522059fa_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"340\" height=\"514\" \/><br \/>The co-ordinates of O in both cases are not same.<br \/>It is not a parallelogram and also not a rhombus.<\/p>\n<p>Question 25.<br \/>In what ratio does the point (-4, 6) divide the line segment joining the points A (-6, 10) and B (3, -8) ?<br \/>Solution:<br \/>Let the point P (-4, 6) divides the line segment joining the points A (-6, 10) and B (3, -8) in the ratio m<sub>1<\/sub>\u00a0: m<sub>2<\/sub><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1729\/40918355880_9b69377497_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"327\" height=\"258\" \/><\/p>\n<p>Question 26.<br \/>Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also, find the coordinates of the point of division.<br \/>Solution:<br \/>The points lies on y-axis<br \/>Let its coordinates be (0, y)<br \/>and let it divides the line segment joining the points (5, -6) and (-1, -4) in the ratio m<sub>1<\/sub>\u00a0: m<sub>2<\/sub><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1729\/40918356190_506cb167eb_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"356\" height=\"405\" \/><\/p>\n<p>Question 27.<br \/>Show that A (-3, 2), B (-5, -5), C (2, -3) and D (4, 4) are the vertices of a rhombus.<br \/>Solution:<br \/>Vertices of a quadrilateral ABCD are A (-3, 2), B (-5, -5), C (2, -3) and D (4, 4)<br \/>Join the diagonals AC and BD which intersect each other at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/27859776427_2b261cc151_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"354\" height=\"547\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/40918356560_94e07fc65e_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"317\" height=\"312\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1722\/40918356800_3be5af56f6_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"353\" height=\"226\" \/><\/p>\n<p>Question 28.<br \/>Find the lengths of the medians of a \u2206ABC having vertices A (0, -1), B (2, 1) and C (0, 3).<br \/>Solution:<br \/>A (0, -1), B (2, 1) and C (0, 3) are the vertices of \u2206ABC<br \/>Let D, E and F are the mid points of BC, CA and AB respectively<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1751\/27859776687_3721b8c855_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"335\" height=\"546\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1727\/27859776497_5b87ddc01a_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"312\" height=\"306\" \/><\/p>\n<p>Question 29.<br \/>Find the lengths of the medians of a \u2206ABC, having the vertices at A (5, 1), B (1, 5) and C (3,-1).<br \/>Solution:<br \/>A (5, 1), B (1, 5) and C (3, -1) are the vertices of \u2206ABC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1754\/27859777087_6f29fa2968_o.png\" alt=\"RD Sharma 10 Chapter 14 Co-Ordinate Geometry\" width=\"328\" height=\"529\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/27859776907_d6e9454673_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"346\" height=\"462\" \/><\/p>\n<p>Question 30.<br \/>Find the co-ordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.<br \/>Solution:<br \/>AB is a line segment whose ends points are A (-4, 0) and B (0, 6)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1732\/27859777397_5ea5c10343_o.png\" alt=\"RD Sharma 10 Chapter 14 Co-Ordinate Geometry\" width=\"349\" height=\"376\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/27859777207_6bb3315853_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"331\" height=\"204\" \/><\/p>\n<p>Question 31.<br \/>Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).<br \/>Solution:<br \/>Let M be the mid point of AB. Co-ordinates of the mid point of this line segment joining two points A (5, 7) and B (3, 9)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/28855245008_26eaca7b93_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 14 Co-Ordinate Geometry\" width=\"333\" height=\"279\" \/><\/p>\n<p>Question 32.<br \/>Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4).<br \/>Solution:<br \/>Let M be the mid-point of the line segment joining the points (6, 8) and (2, 4)<br \/>Now co-ordinates of M will be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1742\/28855245448_8d9b8b80e6_o.png\" alt=\"Class 10 RD Sharma Chapter 14 Co-Ordinate Geometry\" width=\"309\" height=\"129\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1755\/27859777737_3d375292f2_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 14 Co-Ordinate Geometry\" width=\"346\" height=\"184\" \/><\/p>\n<p>Question 33.<br \/>If A and B are (1, 4) and (5, 2) respectively, find the co-ordinates of P When\u00a0APBP\u00a0=\u00a034<br \/>Solution:<br \/>Point P divides the line segment joining the points (1, 4) and (5, 2) in the ratio of AP : PB = 3 : 4<br \/>Co-ordinates of P will be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1734\/28855245838_3797355758_o.png\" alt=\"Class 10 RD Sharma Chapter 14 Co-Ordinate Geometry\" width=\"260\" height=\"192\" \/><\/p>\n<p>Question 34.<br \/>Show that the points A (1, 0), B (5, 3), C (2, 7) and D (-2, 4) are the vertices of a parallelogram.<br \/>Solution:<br \/>If ABCD is a parallelogram, then its diagonal<br \/>AC and BD bisect eachother at O<br \/>Let O is the mid-point of AC, then co<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1752\/28855246308_e62e76ee8c_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"328\" height=\"214\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1755\/28855246028_1e16cb87f3_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"347\" height=\"440\" \/><\/p>\n<p>Question 35.<br \/>Determine the ratio in which the point P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also find the value of m. [CBSE 2004]<br \/>Solution:<br \/>Let the ratio be r : s in which P (m, 6) divides the line segment joining the points A (-4, 3) and B (2, 8)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1754\/27859779027_8903a2a6b3_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"285\" height=\"344\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1741\/27859778727_ccf9954894_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"217\" height=\"177\" \/><\/p>\n<p>Question 36.<br \/>Determine the ratio in which the point (-6, a) divides the join of A (-3, -1) and B (-8, 9). Also find the value of a. [CBSE 2004]<br \/>Solution:<br \/>Let the point P (-6, a) divides the join of A (-3, -1) and B (-8, 9) in the ratio m : n<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/27859779187_f245e62fa9_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 14 Co-Ordinate Geometry \" width=\"340\" height=\"342\" \/><\/p>\n<p>Question 37.<br \/>ABCD is a rectangle formed by joining the points A (-1, -1), B (-1, 4), C (5, 4) and D (5, -1). P, Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square ? a rectangle ? or a rhombus ? Justify your answer.<br \/>Solution:<br \/>ABCD is a rectangle whose vertices are A (-1,-1), B (-1,4), C (5, 4) and D (5, -1) P, Q, R, and S are the mid-points of the sides AB, BC, CD and DA respectively and are joined PR and QS are also joined.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1723\/42010909404_ae39bea024_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 14 Co-Ordinate Geometry\" width=\"312\" height=\"581\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1745\/41828944025_c721820e64_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"333\" height=\"384\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1750\/42010908514_e8d54f7195_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"339\" height=\"512\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1728\/42010909014_ff0182c46d_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"342\" height=\"356\" \/><\/p>\n<p>Question 38.<br \/>Points P, Q, R and S divide the line segment joining the pionts A (1, 2) and B (6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R. [CBSE 2014]<br \/>Solution:<br \/>Points P, Q, R and S divides AB in 5 equal parts and let coordinates of P, Q, R and S be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1752\/42010909774_ea22b041ec_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"349\" height=\"604\" \/><br \/>Coordinates of R are (4, 5)<\/p>\n<p>Question 39.<br \/>If A and B are two points having co-ordinates (-2, -2) and (2, -4) respectively, find the co-ordinates of P such that AP =\u00a037\u00a0AB<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1729\/42010910114_e21511e793_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry\" width=\"346\" height=\"129\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/42010909994_ed0d9230aa_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry\" width=\"358\" height=\"395\" \/><\/p>\n<p>Question 40.<br \/>Find the co-ordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.<br \/>Solution:<br \/>Let P, Q and R divides the line segment AB in four equal parts<br \/>Co-ordinates of A are (-2, 2) and of B are (2, 8)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1733\/28855250008_e5341429c6_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"337\" height=\"388\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1746\/42010910264_c3d361dbaf_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma\" width=\"334\" height=\"193\" \/><\/p>\n<p>Question 41.<br \/>Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3). Find the fourth vertex.<br \/>Solution:<br \/>Let the co-ordinates of three vertices are A (-2, -1), B (1, 0) and C (4, 3)<br \/>and let the diagonals AC and BD bisect each other at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1759\/42010910634_0312f7f2ea_o.png\" alt=\"RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"343\" height=\"613\" \/><br \/>and\u00a0y2\u00a0= 1 =&gt; y = 2<br \/>Co-ordinates of D will be (1, 2)<\/p>\n<p>Question 42.<br \/>The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the co-ordinates of the fourth vertex.<br \/>Solution:<br \/>Let the extremities of a diagonal AC of a parallelogram ABCD are A (3, -4) and C (-6, 2)<br \/>Let AC and BD bisect eachother at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1749\/41828946195_d2976392a4_o.png\" alt=\"Co-Ordinate Geometry Class 10 RD Sharma\" width=\"350\" height=\"459\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1741\/41828946025_631c6be16a_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry Exercise 14.3\" width=\"281\" height=\"196\" \/><\/p>\n<p>Question 43.<br \/>If the co-ordinates of the mid-points of the sides of a triangle are (1, 1), (2, -3) and (3, 4), find the vertices of the triangle.<br \/>Solution:<br \/>Let A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>) and C (x<sub>3<\/sub>, y<sub>3<\/sub>) be the vertices of the \u2206ABC<br \/>D, E and F are the mid-points of BC, CA and AB respectively such that their co-ordinates are D (1, 1), E (2, -3) and F (3, 4)<br \/>D is mid-point of BC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1731\/40918367750_62124d237b_o.png\" alt=\"RD Sharma Class 10 Solutions Co-Ordinate Geometry Exercise 14.3\" width=\"290\" height=\"523\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1731\/40918367130_f8985b7e6e_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 14 Co-Ordinate Geometry\" width=\"335\" height=\"198\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1727\/40918367390_177c99c1f6_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 14 Co-Ordinate Geometry \" width=\"349\" height=\"351\" \/><\/p>\n<p>Question 44.<br \/>Determine the ratio in which the straight line x \u2013 y \u2013 2 = 0 divides the line segment joining (3, -1) and (8, 9).<br \/>Solution:<br \/>Let the straight line x \u2013 y \u2013 2 = 0 divides the line segment joining the points (3, -1), (8, 9) in the ratio m : n<br \/>Co-ordinates of the point will be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1747\/40918367990_43c9357c08_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 14 Co-Ordinate Geometry \" width=\"351\" height=\"451\" \/><\/p>\n<p>Question 45.<br \/>Three vertices of a parallelogram are (a + b, a \u2013 b), (2 a + b, 2a \u2013 b), (a \u2013 b, a + b). Find the fourth vertex.<br \/>Solution:<br \/>In parallelogram ABCD co-ordinates are of A (a + b, a \u2013 b), B (2a + b, 2a \u2013 b), C (a \u2013 b, a + b)<br \/>Let co-ordinates of D be (x, y)<br \/>Join diagonal AC and BD<br \/>Which bisect eachother at O<br \/>O is the mid-point of AC as well as BD<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1727\/40918368460_bff095f0a9_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 14 Co-Ordinate Geometry\" width=\"353\" height=\"479\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1741\/42728743861_fb8e8c7120_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 14 Co-Ordinate Geometry \" width=\"320\" height=\"184\" \/><\/p>\n<p>Question 46.<br \/>If two vertices of a parallelogram are (3, 2), (-1, 0) and the diagonals cut at (2, -5), find the other vertices of the parallelogram.<br \/>Solution:<br \/>Two vertices of a parallelogram ABCD are A (3,2), and B (-1, 0) and its diagonals bisect each other at O (2, -5)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1733\/41828947415_4d8f4a2930_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"336\" height=\"418\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1741\/41828947175_0bc1a8ed0f_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 14 Co-Ordinate Geometry\" width=\"323\" height=\"245\" \/><\/p>\n<p>Question 47.<br \/>If the co-ordinates of the mid-points of the sides of a triangle ar6 (3, 4), (4, 6) and (5, 7), find its vertices. [CBSE 2008]<br \/>Solution:<br \/>The co-ordinates of the mid-points of the sides BC, CA and AB are D (3, 4), E (4, 6) and F (5, 7) of the \u2206ABC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1753\/42728745731_0c9e624b13_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"345\" height=\"601\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/27859784267_8c7d8a4b66_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"364\" height=\"362\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1734\/27859784377_685766472e_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"351\" height=\"275\" \/><\/p>\n<p>Question 48.<br \/>The line segment joining the points P (3, 3) and Q (6, -6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k. [CBSE 2009]<br \/>Solution:<br \/>Two points A and B trisect the line segment joining the points P (3, 3) and Q (6, -6) and A is nearer to P<br \/>and A lies also on the line 2x + y + k = 0<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1744\/42728746121_b159c2ec58_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 14 Co-Ordinate Geometry\" width=\"346\" height=\"493\" \/><br \/>=&gt; k = -8<br \/>Hence k = -8<\/p>\n<p>Question 49.<br \/>If three consecutive vertices of a parallelogram are (1, -2), (3, 6) and (5, 10), find its fourth vertex.<br \/>Solution:<br \/>A (1, -2), B (3, 6) and C (5, 10) are the three consecutive vertices of the parallelogram ABCD<br \/>Let (x, y) be its fourth vertex<br \/>AC and BD are its diagonals which bisect each other at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1760\/27859785317_327e6874ef_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 14 Co-Ordinate Geometry\" width=\"360\" height=\"554\" \/><\/p>\n<p>Question 50.<br \/>If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.<br \/>Solution:<br \/>A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD<br \/>Diagonals AC and BD bisect eachother at O<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1726\/42728746941_9f5c38e03a_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"316\" height=\"437\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1759\/27859785467_9ab6a717af_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry \" width=\"339\" height=\"253\" \/><\/p>\n<p>Question 51.<br \/>If the co-ordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the co-ordinates of its vertices.<br \/>Solution:<br \/>In a \u2206ABC,<br \/>D, E and F are the mid-points of the sides BC, CA and AB respectively and co-ordinates of D, E and F are (3, -2), (-3, 1) and (4, -3) respectively<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1735\/27859786347_f1b5c14642_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"359\" height=\"601\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1724\/27859785837_38ca914249_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"355\" height=\"374\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1748\/42010913974_e27678d493_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"353\" height=\"123\" \/><\/p>\n<p>Question 52.<br \/>The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the co-ordinates of P and Q are (p, -2) and (53\u00a0, q) respectively, find the values of p and q. [CBSE 2005]<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1728\/41828949505_782441274f_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"350\" height=\"533\" \/><\/p>\n<p>Question 53.<br \/>The line joining the points'(2, 1), (5, -8) is trisected at the points P and Q. If point P lies on the line 2x \u2013 y + k = 0, find the value of k. [CBSE 2005]<br \/>Solution:<br \/>Points A (2, 1), and B (5, -8) are the ends points of the line segment AB<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1724\/42728748621_f00a3096b5_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"351\" height=\"499\" \/><\/p>\n<p>Question 54.<br \/>A (4, 2), B (6, 5) and C (1, 4) are the vertices of \u2206ABC,<br \/>(i) The median from A meets BC in D. Find the coordinates of the point D.<br \/>(ii) Find the coordinates of point P on AD such that AP : PD = 2 : 1.<br \/>(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.<br \/>(iv) What do you observe? [NCERT,CBSE, 2009, 10]<br \/>Solution:<br \/>In \u2206ABC, co-ordinates of A (4, 2) of (6, 5) and of (1, 4) and AD is BE and CF are the medians such that D, E and F are the mid points of the sides BC, CA and AB respectively<br \/>P is a point on AD such that AP : PD = 2 : 1<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1755\/41828950535_59725336a9_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"305\" height=\"558\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/41828949825_40a361f228_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"362\" height=\"390\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1752\/28855256558_98c24951e9_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"346\" height=\"412\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1753\/42679496602_ec81b70209_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 14 Co-Ordinate Geometry\" width=\"337\" height=\"241\" \/><br \/>(iv) We see that co-ordinates of P, Q and R are same i.e., P, Q and R coincides eachother. Medians of the sides of a triangle pass through the same point which is called the centroid of the triangle.<\/p>\n<p>Question 55.<br \/>If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.<br \/>Solution:<br \/>The diagonals of a parallelogram bisect each other<br \/>O is the mid-point of AC and also of BD<br \/>O is the mid-point of AC<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1757\/41828950735_b40c76c0b4_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 14 Co-Ordinate Geometry\" width=\"309\" height=\"488\" \/><\/p>\n<p>Question 56.<br \/>A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that\u00a0APPB\u00a0=\u00a0k1. If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]<br \/>Solution:<br \/>Point P divides the line segment by joining the points A (3, -5) and B (-4, 8)<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1728\/42010916814_4eeb207670_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"304\" height=\"248\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1736\/42728751221_e121aa6a34_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 14 Co-Ordinate Geometry\" width=\"350\" height=\"230\" \/><\/p>\n<p>Question 57.<br \/>The mid-point P of the line segment joining the points A (-10, 4) and B (-2, 0) lies on the line segment joining the pionts C (-9, -4) and D (-4, y). Find the ratio in which P divides CD. Also, find the value of y. [CBSE 2014]<br \/>Solution:<br \/>P is the mid-point of line segment joining the points A (-10, 4) and B (-2, 0)<br \/>Coordinates of P will be<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1729\/42728752261_b824f82a4e_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 14 Co-Ordinate Geometry\" width=\"352\" height=\"525\" \/><br \/>=&gt; y =\u00a0183\u00a0= 6<br \/>y = 6<\/p>\n<p>Question 58.<br \/>If the point C (-1, 2) divides internally the line segment joining the points A (2, 5) and B (x, y) in the ratio 3 : 4, find the value of x\u00b2 + y\u00b2. [CBSE 2016]<br \/>Solution:<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1721\/42728752461_780dbb34f7_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 14 Co-Ordinate Geometry\" width=\"356\" height=\"359\" \/><\/p>\n<p>Question 59.<br \/>ABCD is a parallelogram with vertices A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>) and C (x<sub>3<\/sub>, y<sub>3<\/sub>). Find the coordinates of the fourth vertex D in terms of x<sub>1<\/sub>, x<sub>2<\/sub>, x<sub>3<\/sub>, y<sub>1<\/sub>, y<sub>2<\/sub>\u00a0and y<sub>3<\/sub>. [NCERT Exemplar]<br \/>Solution:<br \/>Let the coordinates of D be (x, y). We know that diagonals of a parallelogram bisect each other.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1731\/42728753091_4401f29fb6_o.png\" alt=\"RD Sharma 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"253\" height=\"192\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1747\/42728752891_246d761e46_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 14 Co-Ordinate Geometry\" width=\"638\" height=\"168\" \/><\/p>\n<p>Question 60.<br \/>The points A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>) and C (x<sub>3<\/sub>, y<sub>3<\/sub>) are the vertices of \u2206ABC.<br \/>(i) The median from A meets BC at D. Find the coordinates of the point D.<br \/>(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.<br \/>(iii) Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.<br \/>(iv) What are the coordinates of the centroid of the triangle ABC? [NCERT Exemplar]<br \/>Solution:<br \/>Given that, the points A (x<sub>1<\/sub>, y<sub>1<\/sub>), B (x<sub>2<\/sub>, y<sub>2<\/sub>) and C (x<sub>3<\/sub>, y<sub>3<\/sub>) are the vertices of \u2206ABC.<br \/>(i) We know that, the median bisect the line segment into two equal parts i.e., here D is the mid-point of BC.<br \/><img src=\"https:\/\/farm2.staticflickr.com\/1757\/42728754411_d1305dbaee_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"735\" height=\"524\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1757\/42728753501_6f96861788_o.png\" alt=\"RD Sharma 10 Chapter 14 Co-Ordinate Geometry\" width=\"733\" height=\"501\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1737\/42728753741_fa11bba12f_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 14 Co-Ordinate Geometry\" width=\"724\" height=\"475\" \/><br \/><img src=\"https:\/\/farm2.staticflickr.com\/1731\/42728754041_57a564a37e_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 14 Co-Ordinate Geometry\" width=\"546\" height=\"211\" \/><\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-14-exercise-143\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631771882576\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-the-rd-sharma-class-10-solutions-chapter-14-exercise-143-available-on-the-kopykitab-website\"><\/span>Is the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 available on the Kopykitab website?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the PDFs of RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 are available. These solutions are created in a unique method by Kopykitab\u2019s expert faculty.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631772010486\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-10-solutions-chapter-14-exercise-143-free-pdf\"><\/span>Where can I get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631772079722\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-students-depend-on-the-rd-sharma-class-10-solutions-chapter-14-exercise-143-for-their-exam-preparations-from-kopykitab\"><\/span>Can students depend on the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 for their exam preparations from Kopykitab?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, students can trust the RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3 on the Kopykitab website since subject matter experts have created the solutions in accordance with the most recent CBSE guidelines and exam patterns. Furthermore, students can swiftly study the main concepts of the chapters in both online and offline formats at any time and from anywhere.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 14 Exercise 14.3:\u00a0The majority of the problems in this exercise are based on section formulae. The RD Sharma Class 10 Solutions is an excellent resource for learning how to solve such problems correctly. Students can also use the RD Sharma Solutions for Class 10 Maths Chapter 14 Co-ordinate Geometry &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.3 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-14-exercise-14-3\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry Exercise 14.3 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":128398,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128340"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=128340"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128340\/revisions"}],"predecessor-version":[{"id":128426,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128340\/revisions\/128426"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/128398"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=128340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=128340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=128340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}