{"id":9386,"date":"2018-02-09T17:10:23","date_gmt":"2018-02-09T11:40:23","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9386"},"modified":"2018-11-02T12:57:48","modified_gmt":"2018-11-02T07:27:48","slug":"straight-lines-class-11-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/","title":{"rendered":"Straight Lines class 11 Notes Mathematics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 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\" style=\"cursor:inherit\">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=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" 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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-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:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#Straight_Lines_class_11_Notes_Mathematics\" >Straight Lines class 11 Notes Mathematics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#CBSE_Class_11_Mathematics_Revision_Notes_Chapter-10_Straight_Lines\" >CBSE Class 11 Mathematics Revision Notes Chapter-10 Straight Lines<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#First_Degree_Equation\" >First Degree Equation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#Various_forms_of_equations_of_a_line\" >Various forms of equations of a line:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#CONCURRENT_LINES\" >CONCURRENT LINES<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/#CBSE_Class-11_Revision_Notes_and_Key_Points\" >CBSE Class-11 Revision Notes and Key Points<\/a><\/li><\/ul><\/nav><\/div>\n<p>CBSE Mathematics Chapter 10 Straight Lines class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Straight Lines class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 10 Straight Lines class 11 Notes Mathematics are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Straight_Lines_class_11_Notes_Mathematics\"><\/span>Straight Lines class 11 Notes Mathematics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>apter 10 Straight Lines Download CBSE class 11th revision notes for Chapter 10 Straight Lines class 11 Notes Mathematics in PDF format for free. Download revision notes for Straight Lines class 11 Notes Mathematics and score high in exams. These are the Straight Lines class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong>Revision Notes for Class 11 Mathematics\u00a0<a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Download as PDF<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_11_Mathematics_Revision_Notes_Chapter-10_Straight_Lines\"><\/span><strong>CBSE Class 11 Mathematics Revision Notes Chapter-10 Straight Lines<br \/>\n<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li><strong>Slope of a Line <\/strong><\/li>\n<li><strong>Various Forms of the Equation of a Line <\/strong><\/li>\n<li><strong>General Equation of a Line and Distance of a Point From a Line<\/strong><\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"First_Degree_Equation\"><\/span><strong>First Degree Equation<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Every first degree equation like <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?ax+by+c=0\" \/><\/span><\/span>\u00a0would be the equation of a straight line.<\/p>\n<p><strong>Slope of\u00a0a line<\/strong><\/p>\n<ul>\n<li>Slope (m) of a non-vertical line passing through the points <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {{\\text{x}}_{1}}\\text{ },\\text{ }{{\\text{y}}_{1}}\\text{ } \\right)\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {{\\text{x}}_{2}}\\text{ },\\text{ }{{\\text{y}}_{2}} \\right)\" \/><\/span><\/span>\u00a0is given by is given by\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{m }=\\frac{{{y}_{1}}-{{y}_{2}}}{{{x}_{1}}-{{x}_{2}}}\\text{= }\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{x}_{1}}\\ne {{x}_{2}}\" \/><\/span><\/span>.<\/li>\n<\/ul>\n<ul>\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 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{m =tan}\\alpha \\text{, }\\alpha \\ne \\text{9}{{\\text{0}}^{o}}\\text{ }\" \/><\/span><\/span><\/li>\n<\/ul>\n<ul>\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 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\text{L}}_{1}}\\text{ and }{{\\text{L}}_{2}}\" \/><\/span><\/span>\u00a0with slopes <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\text{m}}_{1}}\\text{ and }{{\\text{m}}_{2}}\" \/><\/span><\/span>\u00a0is given by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\tan \\theta =\\left| \\frac{{{m}_{2}}-{{m}_{1}}}{1+{{m}_{1}}{{m}_{2}}} \\right|\" \/><\/span><\/span>, <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?1+{{m}_{1}}{{m}_{2}}\\ne 0\" \/><\/span><\/span><\/li>\n<\/ul>\n<ul>\n<li>Two lines are parallel if and only if their slopes are equal i.e., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{m_1} = {m_2}\" \/><\/span><\/span><\/li>\n<li>Two lines are <em>perpendicular<\/em> if and only if product of their slopes is \u20131, i.e., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{m_1}.{m_2} = - 1\" \/><\/span><\/span><\/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\u00a0 or y = \u2013 a.<\/li>\n<\/ul>\n<ul>\n<li>Equation of the vertical line having distance\u00a0 b from the\u00a0 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 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {{\\text{x}}_{o}},\\text{ }{{\\text{y}}_{0}}\\text{ } \\right),\" \/><\/span><\/span>\u00a0if and only if its coordinates satisfy the equation.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Various_forms_of_equations_of_a_line\"><\/span><strong>Various forms of equations of a line<\/strong>:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><strong>Two points form<\/strong>:\u00a0Equation of the line passing through the points <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {{\\text{x}}_{1}},\\text{ }{{\\text{y}}_{1}} \\right)\" \/><\/span><\/span>\u00a0and (<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{(}{{\\text{x}}_{2}},\\text{ }{{\\text{y}}_{2}})\" \/><\/span><\/span>\u00a0is given by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y-{{y}_{1}}=\\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}(x-{{x}_{1}})\" \/><\/span><\/span><\/li>\n<li><strong>Slope-Intercept form<\/strong>: The point (x, y) on the line with slope m and y-intercept c lies on the line if and only\u00a0 if\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y=\\text{mx +c}\" \/><\/span><\/span>.<\/li>\n<li>If a line with slope m makes\u00a0 x-intercept\u00a0 d. Then equation of the line\u00a0 is <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y=\\text{m(x -d)}\" \/><\/span><\/span>.<\/li>\n<li><strong>Intercept form<\/strong>: Equation of a line making intercepts\u00a0 a and\u00a0 b on the\u00a0 x-and\u00a0 y-axis, respectively, is\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{x}{a}+\\frac{y}{b}=1\" \/><\/span><\/span>.<\/li>\n<li><strong>Normal form<\/strong>: The equation of the line having normal distance from origin p and angle between normal and the positive <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{x}-\\text{axis }\\omega\" \/><\/span><\/span>\u00a0is given by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{ x cos}\\omega \\text{ +ysin }\\omega =p\" \/><\/span><\/span><\/li>\n<li><strong>General Equation of a Line<\/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><strong>Working Rule for reducing general form into the normal form<\/strong>:<\/li>\n<\/ul>\n<p>(i)\u00a0\u00a0\u00a0\u00a0 Shift constant &#8216;C&#8217; to the R.H.S. and get <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Ax+By=-C\" \/><\/span><\/span><\/p>\n<p>(ii)\u00a0\u00a0\u00a0 If the R.H.S. is not positive, then make it positive by multiplying the whole\u00a0equation\u00a0by -1.<\/p>\n<p>(iii)\u00a0\u00a0 Divide both sides of equation by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\sqrt {{{\\rm{A}}^2} + {{\\rm{B}}^2}}\" \/><\/span><\/span>.<\/p>\n<p>The equation so obtained is in the normal form.<\/p>\n<ul>\n<li><strong>Parametric Equation (Symmetric Form)<\/strong>: <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{x - {x_1}} \\over {\\cos \\theta }} = {{y - {y_1}} \\over {\\sin \\theta }} = r\" \/><\/span><\/span><\/li>\n<li><strong>Equation of a line through origin<\/strong>: <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y=mx\" \/><\/span><\/span>\u00a0or <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y = x\\tan \\theta\" \/><\/span><\/span>.<\/li>\n<li>The perpendicular distance (d) of a line Ax + By+ C = 0 from a point <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~~\\left( {{\\text{x}}_{1}},~{{\\text{y}}_{1}} \\right)\" \/><\/span><\/span>\u00a0is given\u00a0 by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?d=\\frac{\\left| A{{x}_{1}}+B{{y}_{1}}+C \\right|}{\\sqrt{{{A}^{2}}+{{B}^{2}}}}\" \/><\/span><\/span><\/li>\n<li>Distance between the parallel lines\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{Ax }+\\text{ By }+\\text{ }{{\\text{C}}_{1}}\" \/><\/span><\/span>= 0 and = 0, is given by\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?d=\\frac{\\left| {{C}_{1}}-{{C}_{2}} \\right|}{\\sqrt{{{A}^{2}}+{{B}^{2}}}}\" \/><\/span><\/span><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"CONCURRENT_LINES\"><\/span><strong>CONCURRENT LINES<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>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>Condition of concurrency of three lines<\/strong>:<\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{a_1}\\left( {{b_2}{c_3} - {b_3}{c_2}} \\right) + {b_1}\\left( {{c_2}{a_3} - {c_3}{a_2}} \\right) + {c_1}\\left( {{a_2}{b_3} - {a_3}{b_2}} \\right) = 0\" alt=\"Straight Lines class 11 Notes Mathematics\" width=\"406\" height=\"18\" \/><\/span><\/span><\/p>\n<p><strong>EQUATIONS OF FAMILY OF LINES THROUGH THE INTERSECTION OF TWO LINES<\/strong><\/p>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{A}}_1}x + {{\\rm{B}}_1}y + {{\\rm{C}}_1} + k\\left( {{{\\rm{A}}_2}x + {{\\rm{B}}_2}y + {{\\rm{C}}_2}} \\right) = 0\" \/><\/span><\/span><\/p>\n<p>where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?k\" \/><\/span><\/span>\u00a0is a constant and also called parameter.<\/p>\n<p>This equation is of first degree of\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y\" \/><\/span><\/span>, therefore, it represents a family of lines.<\/p>\n<p><strong>DISTANCE BETWEEN TWO PARALLEL LINES<\/strong><\/p>\n<p>Working Rule to find the distance between two parallel lines:<\/p>\n<p>(i)\u00a0\u00a0Find the co-ordinates of any point on one of ht egiven line, preferably by putting \u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?y=0\" \/><\/span><\/span>.<\/p>\n<p>(ii)\u00a0The perpendicular distance of this point from the other line is the required distance between the lines.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-11_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-11 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Straight Lines class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-mathematics\/1371\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-biology\/1388\/cbse-revision-notes\/7\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-accountancy\/1411\/cbse-revision-notes\/7\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-economics\/1423\/cbse-revision-notes\/7\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-business-studies\/1740\/cbse-revision-notes\/7\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-computer-science\/1852\/cbse-revision-notes\/7\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-informatics-practices\/1874\/cbse-revision-notes\/7\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-geography\/1864\/cbse-revision-notes\/7\/\">Geography<\/a><\/li>\n<\/ul>\n<p>To download Straight Lines class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sets-class-11-notes-mathematics\/\">Sets class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/relations-functions-class-11-notes-mathematics\/\">Relations And Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/trigonometric-functions-class-11-notes-mathematics\/\">Trigonometric Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/principles-mathematical-induction-class-11-notes-mathematics\/\">Principles Of Mathematical Induction class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\">Complex Numbers And Quadratic Equations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-inequalities-class-11-notes-mathematics\/\">Linear Inequalities class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/permutations-combinations-class-11-notes-mathematics\/\">Permutations And Combinations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/\">Binomial Theorem class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sequences-and-series-class-11-notes-mathematics\/\">Sequences And Series class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/conic-sections-class-11-notes-mathematics\/\">Conic Sections class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/limits-and-derivatives-class-11-notes-mathematics\/\">Limits And Derivatives class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mathematical-reasoning-class-11-notes-mathematics\/\">Mathematical Reasoning class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/statistics-class-11-notes-mathematics\/\">Statistics class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-11-notes-mathematics\/\">Probability class 11 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Mathematics Chapter 10 Straight Lines class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Straight Lines class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on &#8230; <a title=\"Straight Lines class 11 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/\" aria-label=\"More on Straight Lines class 11 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9298,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,456],"tags":[457,150,461,426,240,583],"class_list":["post-9386","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-11","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes","tag-straight-lines"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Straight Lines class 11 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Straight Lines class 11 Notes Mathematics Chapter 10 in PDF format for free download. 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