{"id":6061,"date":"2023-08-19T07:54:19","date_gmt":"2023-08-19T07:54:19","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6061"},"modified":"2023-08-19T07:54:19","modified_gmt":"2023-08-19T07:54:19","slug":"ncert-solutions-class-10-maths-chapter-7-coordinate-geometry-ex-7-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-7-coordinate-geometry-ex-7-1\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">Chapter &#8211; 7 (Coordinate Geometry)\u00a0<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 7 Coordinate Geometry <\/strong>Exercise 7.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #ff0000;\"><strong>Chapter : 7 Coordinate Geometry<\/strong> <\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-7-coordinate-geometry-ex-7-2\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 7.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-7-coordinate-geometry-ex-7-3\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 7.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-7-coordinate-geometry-ex-7-4\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 7.4<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">Exercise &#8211; 7.1<\/span><\/strong><\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Find the distance between the following pairs of points:<br \/>\n<\/strong>(i) (2, 3), (4, 1)<br \/>\n(ii) (-5, 7), (-1, 3)<br \/>\n(iii) (a, b), (- a, \u2013 b)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Distance formula to find the distance between two points (x<sub>1<\/sub>, y<sub>1<\/sub>) and (x<sub>2<\/sub>, y<sub>2<\/sub>) is, say d,<br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(x_2&amp;space;-&amp;space;x_1)^2&amp;space;+&amp;space;(y_2&amp;space;-&amp;space;y_1)^2}\" alt=\"\\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) Distance between (2, 3) and (4, 1) is given by<br \/>\n<\/strong>d = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(4&amp;space;-&amp;space;2)^2&amp;space;+&amp;space;(1&amp;space;-&amp;space;3)^2}\" alt=\"\\sqrt{(4 - 2)^2 + (1 - 3)^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2)^2&amp;space;+&amp;space;(-&amp;space;2)^2}\" alt=\"\\sqrt{(2)^2 + (- 2)^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{8}\" alt=\"\\sqrt{8}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}\" alt=\"2\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) Distance between (\u22125, 7) and (\u22121, 3) is given by<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">d = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1&amp;space;+&amp;space;5)^2&amp;space;+&amp;space;(3&amp;space;-&amp;space;7)^2}\" alt=\"\\sqrt{(-1 + 5)^2 + (3 - 7)^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(4)^2&amp;space;+&amp;space;(-&amp;space;4)^2}\" alt=\"\\sqrt{(4)^2 + (- 4)^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{32}\" alt=\"\\sqrt{32}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\sqrt{2}\" alt=\"4\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) Distance between\u00a0(<i>a<\/i>,\u00a0<i>b<\/i>) and (\u2212\u00a0<i>a<\/i>, \u2212\u00a0<i>b<\/i>)\u00a0is given by<br \/>\n<\/strong>d = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(a&amp;space;-(-a))^2&amp;space;+&amp;space;(b&amp;space;-&amp;space;(-b))^2}\" alt=\"\\sqrt{(a -(-a))^2 + (b - (-b))^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2a)^2&amp;space;+&amp;space;(2b)^2}\" alt=\"\\sqrt{(2a)^2 + (2b)^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4a^2&amp;space;+4b^2}\" alt=\"\\sqrt{4a^2 +4b^2}\" align=\"absmiddle\" \/><br \/>\nd = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{a^2+b^2}\" alt=\"2\\sqrt{a^2+b^2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns, A and B, discussed in Section 7.2? <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Distance between points\u00a0(0, 0) and (36, 15)<br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(36-0)^2&amp;space;+&amp;space;(15-0)^2}\" alt=\"\\sqrt{(36-0)^2 + (15-0)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{1296&amp;space;+&amp;space;225}\" alt=\"\\sqrt{1296 + 225}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{1521}\" alt=\"\\sqrt{1521}\" align=\"absmiddle\" \/><br \/>\n= 39<br \/>\nYes, Assume town A at origin point (0, 0).<br \/>\nTherefore, town B will be at point (36, 15) with respect to town A.<br \/>\nAnd hence, as calculated above, the distance between town A and B will be\u00a039 km.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.<br \/>\n<\/strong><strong>Solution &#8211;<\/strong>\u00a0 Let the points (1, 5), (2, 3), and (- 2,-11) be representing the vertices A, B, and C of the given triangle respectively.<br \/>\nLet A = (1, 5), B = (2, 3) and C = (- 2,-11)<br \/>\nFind the distance between points: say AB, BC and CA<br \/>\n\u2234 AB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2-1)^2&amp;space;+&amp;space;(3-5)^2}\" alt=\"\\sqrt{(2-1)^2 + (3-5)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(1)^2&amp;space;+&amp;space;(-2)^2}\" alt=\"\\sqrt{(1)^2 + (-2)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{1+4}\" alt=\"\\sqrt{1+4}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{5}\" alt=\"\\sqrt{5}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-2-2)^2&amp;space;+&amp;space;(-11-3)^2}\" alt=\"\\sqrt{(-2-2)^2 + (-11-3)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-4)^2&amp;space;+&amp;space;(-14)^2}\" alt=\"\\sqrt{(-4)^2 + (-14)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{16&amp;space;+&amp;space;196}\" alt=\"\\sqrt{16 + 196}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{212}\" alt=\"\\sqrt{212}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">CA = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-2-1)^2&amp;space;+&amp;space;(-11-5)^2}\" alt=\"\\sqrt{(-2-1)^2 + (-11-5)^2}\" align=\"absmiddle\" \/> <\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3)^2&amp;space;+&amp;space;(-16)^2}\" alt=\"\\sqrt{(-3)^2 + (-16)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9+256}\" alt=\"\\sqrt{9+256}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{265}\" alt=\"\\sqrt{265}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Since AB + BC \u2260 CA<br \/>\nTherefore, the points (1, 5), (2, 3), and (- 2, \u2013 11) are <strong>not collinear<\/strong>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>4. Check whether (5, \u2013 2), (6, 4) and (7, \u2013 2) are the vertices of an isosceles triangle.<br \/>\n<\/strong><strong>Solution &#8211; <\/strong>Let the points (5, &#8211; 2), (6, 4), and (7, &#8211; 2) are representing the vertices A, B, and C of the given triangle respectively.<br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6-5)^2&amp;space;+&amp;space;(4+2)^2}\" alt=\"\\sqrt{(6-5)^2 + (4+2)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1)^2&amp;space;+&amp;space;(6)^2}\" alt=\"\\sqrt{(-1)^2 + (6)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{37}\" alt=\"\\sqrt{37}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(7-6)^2&amp;space;+&amp;space;(-2-4)^2}\" alt=\"\\sqrt{(7-6)^2 + (-2-4)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1)^2&amp;space;+&amp;space;(6)^2}\" alt=\"\\sqrt{(-1)^2 + (6)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{37}\" alt=\"\\sqrt{37}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">CA = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(7-5)^2&amp;space;+&amp;space;(-2+2)^2}\" alt=\"\\sqrt{(7-5)^2 + (-2+2)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4}\" alt=\"\\sqrt{4}\" align=\"absmiddle\" \/><br \/>\n= 2<br \/>\nTherefore, AB = BC<br \/>\nAs two sides are equal in length, therefore, ABC is <strong>an isosceles triangle<\/strong>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>5. In a classroom, 4 friends are seated at points A, B, C and D, as shown in Fig. 7.8. Champa and Chameli walk into the class, and after observing for a few minutes, Champa asks Chameli, \u201cDon\u2019t you think ABCD is a square?\u201d Chameli disagrees. Using the distance formula, find which of them is correct.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6438\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Que5.png\" alt=\"NCERT Class 10 Maths Solution\" width=\"433\" height=\"458\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Que5.png 433w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Que5-284x300.png 284w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Que5-300x317.png 300w\" sizes=\"auto, (max-width: 433px) 100vw, 433px\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211; <\/strong>From the figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).<br \/>\nFind the distance between points using the distance formula, we get<br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6-3)^2&amp;space;+&amp;space;(7-4)^2}\" alt=\"\\sqrt{(6-3)^2 + (7-4)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{3^2&amp;space;+&amp;space;3^2}\" alt=\"\\sqrt{3^2 + 3^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{18}\" alt=\"\\sqrt{18}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(9-6)^2&amp;space;+&amp;space;(4-7)^2}\" alt=\"\\sqrt{(9-6)^2 + (4-7)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{3^2&amp;space;+(-3)^2}\" alt=\"\\sqrt{3^2 +(-3)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{18}\" alt=\"\\sqrt{18}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">CD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6-9)^2&amp;space;+(1-4)^2}\" alt=\"\\sqrt{(6-9)^2 +(1-4)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3)^2+(-3)^2}\" alt=\"\\sqrt{(-3)^2+(-3)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{18}\" alt=\"\\sqrt{18}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">DA = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6-3)^2&amp;space;+(1-4)^2}\" alt=\"\\sqrt{(6-3)^2 +(1-4)^2}\" align=\"absmiddle\" \/> <\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{3^2&amp;space;+(-3)^2}\" alt=\"\\sqrt{3^2 +(-3)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{18}\" alt=\"\\sqrt{18}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal AC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(3-9)^2&amp;space;+&amp;space;(4-4)^2}\" alt=\"\\sqrt{(3-9)^2 + (4-4)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-6)}^2\" alt=\"\\sqrt{(-6)}^2\" align=\"absmiddle\" \/>\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= 6 <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal BD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6-6)^2&amp;space;+&amp;space;(7-1)^2}\" alt=\"\\sqrt{(6-6)^2 + (7-1)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(6)}^2\" alt=\"\\sqrt{(6)}^2\" align=\"absmiddle\" \/> <\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= 6 <\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">It can be observed that all sides of this quadrilateral ABCD are of the same length and also the diagonals are of the same length.<br \/>\nTherefore, ABCD is a square and hence, Champa was correct<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:<br \/>\n<\/strong>(i) (- 1, \u2013 2), (1, 0), (- 1, 2), (- 3, 0)<br \/>\n(ii) (- 3, 5), (3, 1), (0, 3), (- 1, \u2013 4)<br \/>\n(iii) (4, 5), (7, 6), (4, 3), (1, 2) <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>Solution &#8211;<br \/>\n<\/strong>(i) Let the points (- 1, \u2013 2), (1, 0), ( \u2013 1, 2), and ( \u2013 3, 0) represent the vertices A, B, C, and D of the given quadrilateral, respectively.<br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(1+1)^2&amp;space;+(0+2)^2}\" alt=\"\\sqrt{(1+1)^2 +(0+2)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4+4}\" alt=\"\\sqrt{4+4}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}\" alt=\"2\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1-1)^2&amp;space;+&amp;space;(2-0)^2}\" alt=\"\\sqrt{(-1-1)^2 + (2-0)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4+4}\" alt=\"\\sqrt{4+4}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}\" alt=\"2\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">CD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3+1)^2&amp;space;+&amp;space;(0-2)^2}\" alt=\"\\sqrt{(-3+1)^2 + (0-2)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4+4}\" alt=\"\\sqrt{4+4}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}\" alt=\"2\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">DA = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3+1)^2&amp;space;+&amp;space;(0-2)^2}\" alt=\"\\sqrt{(-3+1)^2 + (0-2)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4+4}\" alt=\"\\sqrt{4+4}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{2}\" alt=\"2\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal AC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1+1)^2&amp;space;+(2+2)^2}\" alt=\"\\sqrt{(-1+1)^2 +(2+2)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{0&amp;space;+16}\" alt=\"\\sqrt{0 +16}\" align=\"absmiddle\" \/><br \/>\n= 4<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal BD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3-1)^2&amp;space;+(0-0)^2}\" alt=\"\\sqrt{(-3-1)^2 +(0-0)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{16+0}\" alt=\"\\sqrt{16+0}\" align=\"absmiddle\" \/><br \/>\n= 4<br \/>\nSide length = AB = BC = CD = DA = 2\u221a2<br \/>\nDiagonal Measure = AC = BD = 4<br \/>\nTherefore, the given points are the vertices of a square.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(ii)<\/strong> Let the points (- 3, 5), (3, 1), (0, 3), and (- 1, \u2013 4) represent the vertices A, B, C, and D of the given quadrilateral, respectively.<br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-3-3)^2&amp;space;+(1-5)^2}\" alt=\"\\sqrt{(-3-3)^2 +(1-5)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{36&amp;space;+&amp;space;16}\" alt=\"\\sqrt{36 + 16}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{13}\" alt=\"2\\sqrt{13}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(0-3)^2&amp;space;+(3-1)^2}\" alt=\"\\sqrt{(0-3)^2 +(3-1)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9&amp;space;+4}\" alt=\"\\sqrt{9 +4}\" align=\"absmiddle\" \/>\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{13}\" alt=\"\\sqrt{13}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">CD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1-0)^2&amp;space;+(-4-3)^2}\" alt=\"\\sqrt{(-1-0)^2 +(-4-3)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{1+49}\" alt=\"\\sqrt{1+49}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?5\\sqrt{2}\" alt=\"5\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">AD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-1+3)^2&amp;space;+(-4-5)^2}\" alt=\"\\sqrt{(-1+3)^2 +(-4-5)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{4+81}\" alt=\"\\sqrt{4+81}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{85}\" alt=\"\\sqrt{85}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">It\u2019s also seen that points A, B and C are collinear.<br \/>\nSo, the given points can only form 3 sides, i.e. a triangle and not a quadrilateral which has 4 sides.<br \/>\nTherefore, the given points cannot form a general quadrilateral.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>(iii)<\/strong> Let the points (4, 5), (7, 6), (4, 3), and (1, 2) represent the vertices A, B, C, and D of the given quadrilateral, respectively.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">AB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(7-4)^2&amp;space;+(6-5)^2}\" alt=\"\\sqrt{(7-4)^2 +(6-5)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9+1}\" alt=\"\\sqrt{9+1}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{10}\" alt=\"\\sqrt{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">BC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(4-7)^2&amp;space;+(3-6)^2}\" alt=\"\\sqrt{(4-7)^2 +(3-6)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9+9}\" alt=\"\\sqrt{9+9}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">CD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(1-4)^2&amp;space;+(2-3)^2}\" alt=\"\\sqrt{(1-4)^2 +(2-3)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9+1}\" alt=\"\\sqrt{9+1}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{10}\" alt=\"\\sqrt{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">AD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(1-4)^2&amp;space;+(2-5)^2}\" alt=\"\\sqrt{(1-4)^2 +(2-5)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9+9}\" alt=\"\\sqrt{9+9}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\sqrt{2}\" alt=\"3\\sqrt{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal AC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(4-4)^2&amp;space;+(3-5)^2}\" alt=\"\\sqrt{(4-4)^2 +(3-5)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{0&amp;space;+4}\" alt=\"\\sqrt{0 +4}\" align=\"absmiddle\" \/><br \/>\n= 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Diagonal BD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(1-7)^2&amp;space;+(2-6)^2}\" alt=\"\\sqrt{(1-7)^2 +(2-6)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{36+16}\" alt=\"\\sqrt{36+16}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\sqrt{13}\" alt=\"2\\sqrt{13}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>7. Find the point on the x-axis which is equidistant from (2, \u2013 5) and (- 2, 9).<br \/>\n<\/strong><strong>Solution &#8211; <\/strong>To find a point on the X-axis.<br \/>\nTherefore, its Y-coordinate will be 0. Let the point on the x-axis be (x,0).<br \/>\nConsider A = (x, 0); B = (2, \u2013 5) and C = (- 2, 9).<br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2-x)^2&amp;space;+&amp;space;(-5-0)^2}\" alt=\"\\sqrt{(2-x)^2 + (-5-0)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2-x)^2&amp;space;+25}\" alt=\"\\sqrt{(2-x)^2 +25}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">AC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-2-x)^2&amp;space;+&amp;space;(9-0)^2}\" alt=\"\\sqrt{(-2-x)^2 + (9-0)^2}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-2-x)^2&amp;space;+&amp;space;81}\" alt=\"\\sqrt{(-2-x)^2 + 81}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">Since both the distance are equal in measure, so AB = AC\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(2-x)^2&amp;space;+25}\" alt=\"\\sqrt{(2-x)^2 +25}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(-2-x)^2&amp;space;+&amp;space;81}\" alt=\"\\sqrt{(-2-x)^2 + 81}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">(2 \u2013 x)<sup>2\u00a0<\/sup>+ 25 = [-(2 + x)]<sup>2\u00a0<\/sup>+ 81<br \/>\n(2 \u2013 x)<sup>2\u00a0<\/sup>+ 25 =\u00a0(2 + x)<sup>2\u00a0<\/sup>+ 81<br \/>\nx<sup>2\u00a0<\/sup>+ 4 \u2013 4x + 25 = x<sup>2\u00a0<\/sup>+ 4 + 4x + 81<br \/>\n8x = 25 \u2013 81 = -56<br \/>\nx = -7<br \/>\nTherefore, the point is (- 7, 0).<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>8. Find the values of y for which the distance between the points P (2, \u2013 3) and Q (10, y) is 10 units.<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong><strong>Given :<\/strong> Distance between (2, \u2013 3) and (10, y) is 10.<br \/>\nUsing the distance formula,<br \/>\nPQ = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{(10-2)^2&amp;space;+(y+3)^2}\" alt=\"\\sqrt{(10-2)^2 +(y+3)^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{8^2&amp;space;+(y+3)^2}\" alt=\"\\sqrt{8^2 +(y+3)^2}\" align=\"absmiddle\" \/><br \/>\nSince PQ = 10\u00a0 <\/span><br \/>\n<span style=\"color: #000000; font-family: Georgia, Palatino;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{8^2&amp;space;+(y+3)^2}\" alt=\"\\sqrt{8^2 +(y+3)^2}\" align=\"absmiddle\" \/> = 10<br \/>\n64 + (y + 3)<sup>2<\/sup> = 100<br \/>\n(y + 3)<sup>2\u00a0<\/sup>= 36<br \/>\ny + 3 = \u00b16<br \/>\ny + 3 = +6 or y + 3 = \u22126<br \/>\ny = 6 \u2013 3 = 3<br \/>\nor<br \/>\ny = \u2013 6 \u2013 3 = -9<br \/>\nTherefore, y = 3 or -9.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>9. If Q (0, 1) is equidistant from P (5, \u2013 3) and R (x, 6), find the values of x. Also, find the distance QR and PR.<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong><strong>Given :<\/strong> Q (0, 1) is equidistant from P (5, \u2013 3) and R (x, 6), which means PQ = QR<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6439\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9.png\" alt=\"\" width=\"335\" height=\"80\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9.png 335w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9-300x72.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><br \/>\nSquaring both sides to omit square root<br \/>\n41 = x<sup>2\u00a0<\/sup>+ 25<br \/>\nx<sup>2\u00a0<\/sup>= 16<br \/>\nx = \u00b1 4<br \/>\nx = 4 or x = -4<br \/>\nCoordinates of Point R will be R (4, 6) or R (-4, 6),<br \/>\nIf R (4, 6), then QR<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6440\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9i.png\" alt=\"\" width=\"485\" height=\"133\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9i.png 485w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans9i-300x82.png 300w\" sizes=\"auto, (max-width: 485px) 100vw, 485px\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\"><strong>10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (- 3, 4).<br \/>\n<\/strong><strong>Solution &#8211; <\/strong>Point (x, y) is equidistant from (3, 6) and (- 3, 4).<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-6441\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans10.png\" alt=\"\" width=\"354\" height=\"76\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans10.png 354w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans10-300x64.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/08\/NCERT-Class-10-Maths-Ex7.1-Ans10-350x76.png 350w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><br \/>\nSquaring both sides,<br \/>\n(x \u2013 3)<sup>2 <\/sup>+ (y \u2013 6)<sup>2<\/sup>\u00a0= (x + 3)<sup>2<\/sup>\u00a0+(y \u2013 4)<sup>2<br \/>\n<\/sup>x<sup>2\u00a0<\/sup>+ 9 \u2013 6x + y<sup>2<\/sup>+ 36 \u2013 12y = x<sup>2\u00a0<\/sup>+ 9 + 6x + y<sup>2\u00a0<\/sup>+16 \u2013 8y<br \/>\n36 \u2013 16 = 6x + 6x + 12y \u2013 8y<br \/>\n20 = 12x + 4y<br \/>\n3x + y = 5<br \/>\n3x + y \u2013 5 = 0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #0000ff; font-family: Georgia, Palatino;\"><b><i><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\">Go Back To Chapters<\/a><\/i><\/b><\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 7 (Coordinate Geometry)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 7 Coordinate Geometry Exercise 7.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 7 Coordinate Geometry NCERT Class 10 Maths Solution Ex &#8211; 7.2 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1086,1087,1044,1049,1048],"class_list":["post-6061","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-7-coordinate-geometry-solutions","tag-ncert-class-10-mathematics-exercise-7-1-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 | TheExamPillar NCERT<\/title>\n<meta name=\"robots\" content=\"index, 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