{"id":68028,"date":"2021-09-02T14:43:00","date_gmt":"2021-09-02T09:13:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68028"},"modified":"2023-11-29T16:52:58","modified_gmt":"2023-11-29T11:22:58","slug":"rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/","title":{"rendered":"RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 (Updated 2023-24)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-123462\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.1.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-23-Exercise-23.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1<\/strong>: \u201cA straight line is a curve such that every point on the line segment joining any two points lies on it is termed as a straight line\u201d. In this chapter, we will discuss concepts related to straight lines, with examples for better understanding. RD Sharma Class 11 Maths Solutions contains all the solutions to the math problems given in the textbook. The subject matter experts have accurately prepared and solved the questions in each section. Students can consult and download <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-the-straight-lines\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 11 Maths Chapter 23<\/a> Exercise 23.1 in PDF from the link given below and start offline practice.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Class 11 Maths Solutions&nbsp;<\/a><\/li>\n<\/ul>\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-69d3316fa914d\" 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\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d3316fa914d\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/#download-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-pdf\" title=\"Download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF:\">Download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/#access-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231\" title=\"Access RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1\">Access RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/#what-are-the-important-topics-included-in-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231\" title=\"What are the important topics included in RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1?\">What are the important topics included in RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/#what-are-the-benefits-of-studying-from-rd-sharma-solutions-class-12\" title=\"What are the benefits of studying from RD Sharma Solutions Class 12?\">What are the benefits of studying from RD Sharma Solutions Class 12?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/#can-i-open-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-pdf-on-my-smartphone\" title=\"Can I open RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF on my smartphone?\">Can I open RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF on my smartphone?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-pdf\"><\/span>Download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<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\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-23-Ex-23.1-1-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-23-Ex-23.1-1-1.pdf\">RD-Sharma-Solutions-Class-11-Maths-Chapter-23-Ex-23.1-1<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231\"><\/span>Access RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Straight Lines Ex 23.1 Q1<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7483\/15958971790_d113b48b5c_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-1\" width=\"400\" height=\"351\"><br><strong>Straight Lines Ex 23.1 Q2<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8645\/15526549573_2372e6c705_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-2\" width=\"379\" height=\"234\"><br><strong>Straight Lines Ex 23.1 Q3(i)<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7570\/15960197009_0f34e1e1df_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-3\" width=\"260\" height=\"228\"><br><strong>Straight Lines Ex 23.1 Q3(ii)<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7546\/15960196939_e095cb81ae_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-3-ii\" width=\"325\" height=\"220\"><br><strong>Straight Lines Ex 23.1 Q3(iii)<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7492\/16120488306_8b367e2aa9_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-3-iii\" width=\"333\" height=\"237\"><br><strong>Straight Lines Ex 23.1 Q3(iv)<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7504\/15523940724_3bea4298a2_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-3-iv\" width=\"378\" height=\"220\"><br><strong>Straight Lines Ex 23.1 Q4<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7564\/15960521547_33ff2565ea_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-4\" width=\"426\" height=\"268\"><br><strong>Straight Lines Ex 23.1 Q5(i)<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7517\/15960196339_926bb72ac9_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-5\" width=\"442\" height=\"234\"><br><strong>Straight Lines Ex 23.1 Q5(ii)<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8561\/15960196319_bbf51328a4_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-5-i\" width=\"513\" height=\"205\"><br><strong>Straight Lines Ex 23.1 Q6<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8673\/15526548393_78e8b701bd_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-6\" width=\"316\" height=\"210\"><br><strong>Straight Lines Ex 23.1 Q7<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7502\/15960195679_d08df34b78_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-7\" width=\"546\" height=\"201\"><br><strong>Straight Lines Ex 23.1 Q8<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7550\/15960520007_c439059871_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-8\" width=\"298\" height=\"183\"><\/p>\n<p><strong>Straight Lines Ex 23.1 Q9<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7566\/15958969560_c20f2d5530_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-9\" width=\"377\" height=\"221\"><br><strong>Straight Lines Ex 23.1 Q10<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8561\/15960194739_b74c19a5e5_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-10\" width=\"349\" height=\"195\"><br><strong>Straight Lines Ex 23.1 Q11<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8662\/16145523522_3393caf97e_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-11\" width=\"383\" height=\"569\"><br><strong>Straight Lines Ex 23.1 Q12<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7485\/16120485596_22176763e4_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-12\" width=\"585\" height=\"283\"><br><strong>Straight Lines Ex 23.1 Q13<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7472\/15960517737_d5145122cb_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-13\" width=\"310\" height=\"594\"><br><strong>Straight Lines Ex 23.1 Q14<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8681\/16145521402_fe2742c94f_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-14\" width=\"446\" height=\"255\"><br><strong>Straight Lines Ex 23.1 Q15<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7580\/15960192429_f9d1147c5f_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-15\" width=\"524\" height=\"218\"><br><strong>Straight Lines Ex 23.1 Q16<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7541\/15523936394_1d11b74348_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-16\" width=\"487\" height=\"311\"><br><strong>Straight Lines Ex 23.1 Q17<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7520\/16144365361_cd823eb1d3_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-17\" width=\"378\" height=\"265\"><br><strong>Straight Lines Ex 23.1 Q18<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7573\/15960517067_c987567d4f_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-18\" width=\"520\" height=\"269\"><br><strong>Straight Lines Ex 23.1 Q19<\/strong><br><img src=\"https:\/\/farm8.staticflickr.com\/7499\/15960192009_18144edfe9_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-19\" width=\"450\" height=\"308\"><br><strong>Straight Lines Ex 23.1 Q20<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8634\/15958827088_4693c51e2f_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-20\" width=\"403\" height=\"393\"><br><strong>Straight Lines Ex 23.1 Q21<\/strong><br><img src=\"https:\/\/farm9.staticflickr.com\/8562\/15526544203_3d21943f0e_o.png\" alt=\"RD-Sharma-class-11-Solutions-Chapter-23-The-Straight-Lines-Ex-23.1-Q-21\" width=\"500\" height=\"454\"><\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong><b>First Degree Equation<\/b><\/strong><\/p>\n<p>Every first degree equation like&nbsp;ax+by+c=0ax+by+c=0&nbsp;would be the equation of a straight line.<\/p>\n<p><strong><b>Slope of a line<\/b><\/strong><\/p>\n<ul>\n<li>Slope (m) of a non-vertical line passing through the points&nbsp;(x1&nbsp;,y1&nbsp;)(x1&nbsp;,&nbsp;y1&nbsp;)&nbsp;and&nbsp;(x2&nbsp;,&nbsp;y2)(x2&nbsp;,&nbsp;y2)&nbsp;is given by is given by&nbsp;m&nbsp;=y1\u2212y2x1\u2212x2=&nbsp;m&nbsp;=y1\u2212y2x1\u2212x2=&nbsp;&nbsp;x1\u2260x2x1\u2260x2.<\/li>\n<li>If a line makes an angle \u00e1 with the positive direction of x-axis, then the slope of the line is given by&nbsp;m =tan\u03b1,&nbsp;\u03b1\u226090om =tan\u03b1,&nbsp;\u03b1\u226090o&nbsp;<\/li>\n<li>Slope of horizontal line is zero and slope of vertical line is undefined.<\/li>\n<li>An acute angle (say \u03b8) between lines&nbsp;L1&nbsp;and&nbsp;L2L1&nbsp;and&nbsp;L2with slopes&nbsp;m1&nbsp;and&nbsp;m2m1&nbsp;and&nbsp;m2&nbsp;is given by&nbsp;tan\u03b8=\u2223\u2223m2\u2212m11+m1m2\u2223\u2223tan\u2061\u03b8=|m2\u2212m11+m1m2|,&nbsp;1+m1m2\u226001+m1m2\u22600<\/li>\n<li>Two lines are parallel if and only if their slopes are equal i.e.,&nbsp;m1=m2m1=m2<\/li>\n<li>Two lines are&nbsp;perpendicularif and only if product of their slopes is \u20131, i.e.,&nbsp;mm2=\u22121m1.m2=\u22121<\/li>\n<li>Three points A, B and C are collinear, if and only if slope of AB = slope of BC.<\/li>\n<li>Equation of the horizontal line having distance a from the x-axis is eithery = a or y = \u2013 a.<\/li>\n<li>Equation of the vertical line having distance b from the y-axis is eitherx = b or x = \u2013 b.<\/li>\n<li>The point (x, y) lies on the line with slope m and through the fixed point&nbsp;(xo,y0&nbsp;),(xo,&nbsp;y0&nbsp;),&nbsp;if and only if its coordinates satisfy the equation.<\/li>\n<\/ul>\n<p><strong><b>Various forms of equations of a line<\/b><\/strong>:<\/p>\n<ul>\n<li><b><\/b><strong><b>Two points form<\/b><\/strong>: Equation of the line passing through the points&nbsp;(x1,y1)(x1,&nbsp;y1)&nbsp;and ((x2,&nbsp;y2)(x2,&nbsp;y2)&nbsp;is given by&nbsp;y\u2212y1=y2\u2212y1x2\u2212x1(x\u2212x1)y\u2212y1=y2\u2212y1x2\u2212x1(x\u2212x1)<\/li>\n<li><b><\/b><strong><b>Slope-Intercept form<\/b><\/strong>: The point (x, y) on the line with slope m and y-intercept c lies on the line if and only if&nbsp;y=mx +cy=mx +c.<\/li>\n<li>If a line with slope m makes x-intercept d. Then equation of the line is&nbsp;y=m(x -d)y=m(x -d).<\/li>\n<li><b><\/b><strong><b>Intercept form<\/b><\/strong>: Equation of a line making intercepts a and b on the x-and y-axis, respectively, is&nbsp;xa+yb=1xa+yb=1.<\/li>\n<li><b><\/b><strong><b>Normal form<\/b><\/strong>: The equation of the line having normal distance from origin p and angle between normal and the positive&nbsp;x\u2212axis&nbsp;\u03c9x\u2212axis&nbsp;\u03c9is given by&nbsp;&nbsp;x cos\u03c9&nbsp;+ysin&nbsp;\u03c9=p&nbsp;x cos\u03c9&nbsp;+ysin&nbsp;\u03c9=p<\/li>\n<li><b><\/b><strong><b>General Equation of a Line<\/b><\/strong>: Any equation of the form Ax + By + C = 0, with A and B are not zero, simultaneously, is called the general linear equation or general equation of a line.<\/li>\n<li><b><\/b><strong><b>Working Rule for reducing general form into the normal form<\/b><\/strong>:<\/li>\n<\/ul>\n<p>(i) Shift constant &#8216;C&#8217; to the R.H.S. and get&nbsp;Ax+By=\u2212CAx+By=\u2212C<br>(ii) If the R.H.S. is not positive, then make it positive by multiplying the whole equation by -1.<br>(iii) Divide both sides of equation by&nbsp;A2+B2\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u221aA2+B2.<\/p>\n<p>The equation so obtained is in the normal form.<\/p>\n<ul>\n<li><b><\/b><strong><b>Parametric Equation (Symmetric Form)<\/b><\/strong>:&nbsp;x\u2212x1cos\u03b8=y\u2212y1sin\u03b8=rx\u2212x1cos\u2061\u03b8=y\u2212y1sin\u2061\u03b8=r<\/li>\n<li><b><\/b><strong><b>Equation of a line through origin<\/b><\/strong>:&nbsp;y=mxy=mxor&nbsp;y=xtan\u03b8y=xtan\u2061\u03b8.<\/li>\n<li>The perpendicular distance (d) of a line Ax + By+ C = 0 from a point&nbsp;(x1,&nbsp;y1)&nbsp;&nbsp;(x1,&nbsp;y1)&nbsp;is given by&nbsp;d=|Ax1+By1+C|A2+B2\u221ad=|Ax1+By1+C|A2+B2<\/li>\n<li>Distance between the parallel lines&nbsp;Ax&nbsp;+&nbsp;By&nbsp;+&nbsp;C1Ax&nbsp;+&nbsp;By&nbsp;+&nbsp;C1= 0 and&nbsp;Ax&nbsp;+&nbsp;By&nbsp;+&nbsp;C2Ax&nbsp;+&nbsp;By&nbsp;+&nbsp;C2= 0, is given by&nbsp;d=|C1\u2212C2|A2+B2\u221ad=|C1\u2212C2|A2+B2<\/li>\n<\/ul>\n<p><strong><b>Concurrent Lines<\/b><\/strong><br>Three of more straight lines are said to be concurrent if they pass through a common point i.e., they meet at a point. Thus, if three lines are concurrent the point of intersection of two lines lies on the third line.<\/p>\n<p><strong><b>Condition of concurrency of three lines<\/b><\/strong>:<br>a1(b2c3\u2212b3c2)+b1(c2a3\u2212c3a2)+c1(a2b3\u2212a3b2)=0a1(b2c3\u2212b3c2)+b1(c2a3\u2212c3a2)+c1(a2b3\u2212a3b2)=0<\/p>\n<p><strong><b>EQUATIONS OF FAMILY OF LINES THROUGH THE INTERSECTION OF TWO LINES<\/b><\/strong><br>A1x+B1y+C1+k(A2x+B2y+C2)=0A1x+B1y+C1+k(A2x+B2y+C2)=0<br>where&nbsp;kk&nbsp;is a constant and also called parameter.<br>This equation is of first degree of&nbsp;xx&nbsp;and&nbsp;yy, therefore, it represents a family of lines.<\/p>\n<p><strong><b>DISTANCE BETWEEN TWO PARALLEL LINES<\/b><\/strong><br>Working Rule to find the distance between two parallel lines:<br>(i) Find the co-ordinates of any point on one of ht egiven line, preferably by putting&nbsp;x=0x=0&nbsp;and&nbsp;y=0y=0.<br>(ii) The perpendicular distance of this point from the other line is the required distance between the lines.<\/p>\n<p>We have included all the information regarding <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1. If you have any query feel free to ask in the comment section.&nbsp;<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231\"><\/span>FAQ: RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630573806681\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-important-topics-included-in-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231\"><\/span>What are the important topics included in RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can refer to the above article. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630573842750\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-benefits-of-studying-from-rd-sharma-solutions-class-12\"><\/span>What are the benefits of studying from RD Sharma Solutions Class 12?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>By practicing these solutions, students can earn higher academic grades. Our experts solve these solutions with utmost accuracy to help students in their studies.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630573844263\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-download-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-pdf-free\"><\/span>Can I download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can download RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630573845229\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-enough-for-class-12-maths\"><\/span>Is RD Sharma enough for Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>RD Sharma is a good book that gives you thousands of questions to practice.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630573874665\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-open-rd-sharma-solutions-class-11-maths-chapter-23-exercise-231-pdf-on-my-smartphone\"><\/span>Can I open RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF on my smartphone?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can open RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 PDF on any device.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1: \u201cA straight line is a curve such that every point on the line segment joining any two points lies on it is termed as a straight line\u201d. In this chapter, we will discuss concepts related to straight lines, with examples for better understanding. RD Sharma &#8230; <a title=\"RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 (Updated 2023-24)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-23-exercise-23-1\/\" aria-label=\"More on RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.1 (Updated 2023-24)\">Read more<\/a><\/p>\n","protected":false},"author":236,"featured_media":123462,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73397,73717,73411,2985,73410],"tags":[3428,73334,73564],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68028"}],"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\/236"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68028"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68028\/revisions"}],"predecessor-version":[{"id":514326,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68028\/revisions\/514326"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/123462"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}