{"id":4975,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/"},"modified":"2023-03-22T15:14:03","modified_gmt":"2023-03-22T09:44:03","slug":"ncert-solutions-class-10-maths-exercise-7-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 7.1"},"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\/ncert-solutions-class-10-maths-exercise-7-1\/#NCERT_Solutions_for_Class_10_Maths_Coordinate_Geometry\" >NCERT Solutions for Class 10 Maths\u00a0Coordinate Geometry<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#1_Find_the_distance_between_the_following_pairs_of_points\" >1. Find the distance between the following pairs of points:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#2_Find_the_distance_between_the_points_0_0_and_36_15_Also_find_the_distance_between_towns_A_and_B_if_town_B_is_located_at_36_km_east_and15_km_north_of_town_A\" >2. Find the distance between the points (0, 0) and (36, 15). Also, find the distance between towns A and B if town B is located at 36 km east and15 km north of town A.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#3_Determine_if_the_points_1_5_2_3_and_%E2%80%932_%E2%80%9311_are_collinear\" >3. Determine if the points (1, 5), (2, 3) and (\u20132, \u201311) are collinear.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#4_Check_whether_5_%E2%80%932_6_4_and_7_%E2%80%932_are_the_vertices_of_an_isosceles_triangle\" >4. Check whether (5, \u20132), (6, 4) and (7, \u20132) are the vertices of an isosceles triangle.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#5_In_a_classroom_4_friends_are_seated_at_the_points_A_3_4_B_6_7_C_9_4_and_D_6_1_Champa_and_Chameli_walk_into_the_class_and_after_observing_for_a_few_minutes_Champa_asks_Chameli_%E2%80%9CDont_you_think_ABCD_is_a_square%E2%80%9DChameli_disagrees_Using_distance_formula_find_which_of_them_is_correct\" >5. In a classroom, 4 friends are seated at the points A (3, 4), B (6, 7), C (9, 4) and D (6, 1). Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli. &#8220;Don&#8217;t you think ABCD is a square?&#8221;Chameli disagrees. Using distance formula, find which of them is correct.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#6_Name_the_type_of_quadrilateral_formed_if_any_by_the_following_points_and_give_reasons_for_your_answer\" >6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#7_Find_the_point_on_the_x%E2%80%93axis_which_is_equidistant_from_2_%E2%80%935_and_%E2%80%932_9\" >7. Find the point on the x\u2013axis which is equidistant from (2, \u20135) and (\u20132, 9).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#8_Find_the_values_of_y_for_which_the_distance_between_the_points_P_2_%E2%80%933_and_Q_10_y_is_10_units\" >8. Find the values of y for which the distance between the points P (2, \u20133) and Q (10, y) is 10 units.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#9_If_Q_0_1_is_equidistant_from_P_5_%E2%80%933_and_R_x_6_find_the_values_of_x_Also_find_the_distances_QR_and_PR\" >9. If, Q (0, 1) is equidistant from P (5, \u20133) and R (x, 6), find the values of x. Also, find the distances QR and PR.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#10_Find_a_relation_between_x_and_y_such_that_the_point_x_y_is_equidistant_from_the_point_3_6_and_%E2%80%933_4\" >10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (\u20133, 4).<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#NCERT_Solutions_for_Class_10_Maths_Exercise_71\" >NCERT Solutions for Class 10 Maths Exercise 7.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-7-1\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 7.1 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Maths\u00a0Coordinate Geometry\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-coordinate-geometry\/1209\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 7.1\" width=\"159\" height=\"196\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Coordinate_Geometry\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Coordinate Geometry<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Find_the_distance_between_the_following_pairs_of_points\"><\/span><strong>1. Find the distance between the following pairs of points:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) (2, 3), (4,1) <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) (\u20135, 7), (\u20131, 3)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) (a, b), (\u2013a, \u2013b)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Applying Distance Formula to find distance between points (2, 3) and (4,1), we get<\/p>\n<p style=\"text-align: justify;\">d = <img decoding=\"async\" style=\"height: 29px; width: 399px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Applying Distance Formula to find distance between points (\u20135, 7) and (\u20131, 3), we get<\/p>\n<p style=\"text-align: justify;\">d = <img decoding=\"async\" style=\"height: 35px; width: 449px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Applying Distance Formula to find distance between points (a, b) and (\u2013a, \u2013b), we get<\/p>\n<p style=\"text-align: justify;\">d = <img decoding=\"async\" style=\"height: 29px; width: 541px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image003.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Find_the_distance_between_the_points_0_0_and_36_15_Also_find_the_distance_between_towns_A_and_B_if_town_B_is_located_at_36_km_east_and15_km_north_of_town_A\"><\/span><strong>2. Find the distance between the points (0, 0) and (36, 15). Also, find the distance between towns A and B if town B is located at 36 km east and15 km north of town A.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Applying Distance Formula to find distance between points (0, 0) and (36, 15), we get<\/p>\n<p style=\"text-align: justify;\">d = <img decoding=\"async\" style=\"height: 35px; width: 434px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">Town B is located at 36 km east and15 km north of town A. So, the location of town A and B can be shown as:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 245\" style=\"height: 212px; width: 258px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image005.jpg\" alt=\"\" \/><\/p>\n<p style=\"text-align: justify;\">Clearly, the coordinates of point A are (0, 0) and coordinates of point B are (36, 15).<\/p>\n<p style=\"text-align: justify;\">To find the distance between them, we use Distance formula:<\/p>\n<p style=\"text-align: justify;\">d = <img decoding=\"async\" style=\"height: 31px; width: 432px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image006.png\" \/>km<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Determine_if_the_points_1_5_2_3_and_%E2%80%932_%E2%80%9311_are_collinear\"><\/span><strong>3. Determine if the points (1, 5), (2, 3) and (\u20132, \u201311) are collinear.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = (1, 5), B = (2, 3) and C = (\u20132, \u201311)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distance AB, BC and CA.<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 312px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 35px; width: 451px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">CA = <img decoding=\"async\" style=\"height: 35px; width: 391px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since AB + AC \u2260 BC, BC + AC <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image010.png\" \/> AB and AC<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image010.png\" \/> BC.<\/p>\n<p style=\"text-align: justify;\">Therefore, the points A, B and C are not collinear.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Check_whether_5_%E2%80%932_6_4_and_7_%E2%80%932_are_the_vertices_of_an_isosceles_triangle\"><\/span><strong>4. Check whether (5, \u20132), (6, 4) and (7, \u20132) are the vertices of an isosceles triangle.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = (5, \u20132), B = (6, 4) and C = (7, \u20132)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distances AB, BC and CA.<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 348px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 31px; width: 351px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\">CA = <img decoding=\"async\" style=\"height: 31px; width: 376px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since AB = BC.<\/p>\n<p style=\"text-align: justify;\">Therefore, A, B and C are vertices of an isosceles triangle.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_In_a_classroom_4_friends_are_seated_at_the_points_A_3_4_B_6_7_C_9_4_and_D_6_1_Champa_and_Chameli_walk_into_the_class_and_after_observing_for_a_few_minutes_Champa_asks_Chameli_%E2%80%9CDont_you_think_ABCD_is_a_square%E2%80%9DChameli_disagrees_Using_distance_formula_find_which_of_them_is_correct\"><\/span><strong>5. In a classroom, 4 friends are seated at the points A (3, 4), B (6, 7), C (9, 4) and D (6, 1). Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli. &#8220;Don&#8217;t you think ABCD is a square?&#8221;Chameli disagrees. Using distance formula, find which of them is correct.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 7\" style=\"height: 288px; width: 290px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image014.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We have A = (3, 4), B = (6, 7), C = (9, 4) and D = (6, 1)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distances AB, BC, CD and DA, we get<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 356px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 31px; width: 366px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\">CD = <img decoding=\"async\" style=\"height: 31px; width: 372px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\">DA = <img decoding=\"async\" style=\"height: 31px; width: 362px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, All the sides of ABCD are equal here. \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">Now, we will check the length of its diagonals.<\/p>\n<p style=\"text-align: justify;\">AC = <img decoding=\"async\" style=\"height: 31px; width: 304px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\">BD = <img decoding=\"async\" style=\"height: 31px; width: 355px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\">So, Diagonals of ABCD are also equal. \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">From (1) and (2), we can definitely say that ABCD is a square.<\/p>\n<p style=\"text-align: justify;\">Therefore, Champa is correct.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Name_the_type_of_quadrilateral_formed_if_any_by_the_following_points_and_give_reasons_for_your_answer\"><\/span><strong>6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) (\u20131, \u20132), (1, 0), (\u20131, 2), (\u20133, 0)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) (\u20133, 5), (3, 1), (0, 3), (\u20131, \u20134)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) (4, 5), (7, 6), (4, 3), (1, 2)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Let A = (\u20131, \u20132), B = (1, 0), C= (\u20131, 2) and D = (\u20133, 0)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distances AB, BC, CD and DA, we get<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 389px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 31px; width: 368px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">CD = <img decoding=\"async\" style=\"height: 31px; width: 400px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\">DA = <img decoding=\"async\" style=\"height: 31px; width: 412px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, all four sides of quadrilateral are equal. \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">Now, we will check the length of diagonals.<\/p>\n<p style=\"text-align: justify;\">AC = <img decoding=\"async\" style=\"height: 31px; width: 393px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">BD = <img decoding=\"async\" style=\"height: 31px; width: 362px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, diagonals of quadrilateral ABCD are also equal. \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">From (1) and (2), we can say that ABCD is a square.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Let A = (\u20133, 5), B= (3, 1), C= (0, 3) and D= (\u20131, \u20134)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distances AB, BC, CD and DA, we get<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 406px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 31px; width: 330px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">CD = <img decoding=\"async\" style=\"height: 31px; width: 415px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">DA = <img decoding=\"async\" style=\"height: 31px; width: 382px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\">We cannot find any relation between the lengths of different sides.<\/p>\n<p style=\"text-align: justify;\">Therefore, we cannot give any name to the quadrilateral ABCD.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Let A = (4, 5), B= (7, 6), C= (4, 3) and D= (1, 2)<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find distances AB, BC, CD and DA, we get<\/p>\n<p style=\"text-align: justify;\">AB = <img decoding=\"async\" style=\"height: 31px; width: 319px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">BC = <img decoding=\"async\" style=\"height: 31px; width: 375px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\">CD = <img decoding=\"async\" style=\"height: 31px; width: 326px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\">DA = <img decoding=\"async\" style=\"height: 31px; width: 372px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here opposite sides of quadrilateral ABCD are equal. \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">We can now find out the lengths of diagonals.<\/p>\n<p style=\"text-align: justify;\">AC = <img decoding=\"async\" style=\"height: 31px; width: 352px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\">BD = <img decoding=\"async\" style=\"height: 31px; width: 408px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here diagonals of ABCD are not equal. \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">From (1) and (2), we can say that ABCD is not a rectangle therefore it is a parallelogram.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Find_the_point_on_the_x%E2%80%93axis_which_is_equidistant_from_2_%E2%80%935_and_%E2%80%932_9\"><\/span><strong>7. Find the point on the x\u2013axis which is equidistant from (2, \u20135) and (\u20132, 9).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let the point be (x, 0) on x\u2013axis which is equidistant from (2, \u20135) and (\u20132, 9).<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula and according to given conditions we have:<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 31px; width: 304px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 27px; width: 250px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">Squaring both sides, we get<\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 22px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image039.png\" \/>= <img decoding=\"async\" style=\"height: 22px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 \u22124x + 29 = 4x + 85<\/p>\n<p style=\"text-align: justify;\">\u21d2 8x = \u221256<\/p>\n<p style=\"text-align: justify;\">\u21d2 x = \u22127<\/p>\n<p style=\"text-align: justify;\">Therefore, point on the x\u2013axis which is equidistant from (2, \u20135) and (\u20132, 9) is (\u20137, 0)<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Find_the_values_of_y_for_which_the_distance_between_the_points_P_2_%E2%80%933_and_Q_10_y_is_10_units\"><\/span><strong>8. Find the values of y for which the distance between the points P (2, \u20133) and Q (10, y) is 10 units.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Using Distance formula, we have<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 29px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 29px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 29px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\">Squaring both sides, we get<\/p>\n<p style=\"text-align: justify;\">100 = <img decoding=\"async\" style=\"height: 24px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image044.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 24px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\">Solving this Quadratic equation by factorization, we can write<\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 24px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 y (y + 9) \u2013 3 (y + 9) = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 (y + 9) (y \u2212 3) = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 y = 3, \u22129<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_If_Q_0_1_is_equidistant_from_P_5_%E2%80%933_and_R_x_6_find_the_values_of_x_Also_find_the_distances_QR_and_PR\"><\/span><strong>9. If, Q (0, 1) is equidistant from P (5, \u20133) and R (x, 6), find the values of x. Also, find the distances QR and PR.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>It is given that Q is equidistant from P and R. Using Distance Formula, we get<\/p>\n<p style=\"text-align: justify;\">PQ = RQ<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image047.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 82px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image047.png\" \/> <img decoding=\"async\" style=\"height: 29px; width: 276px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 29px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 27px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">Squaring both sides, we get<\/p>\n<p style=\"text-align: justify;\">\u21d2 25 + 16 = <img decoding=\"async\" style=\"height: 22px; width: 62px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 22px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 x = 4, \u22124<\/p>\n<p style=\"text-align: justify;\">Thus, Q is (4, 6) or (\u20134, 6).<\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find QR, we get<\/p>\n<p style=\"text-align: justify;\">Using value of x = 4 QR = <img decoding=\"async\" style=\"height: 29px; width: 243px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Using value of x = \u20134 QR = <img decoding=\"async\" style=\"height: 29px; width: 244px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, QR = <img decoding=\"async\" style=\"height: 23px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">Using Distance Formula to find PR, we get<\/p>\n<p style=\"text-align: justify;\">Using value of x = 4 PR = <img decoding=\"async\" style=\"height: 29px; width: 246px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\">Using value of x =\u20134 PR = <img decoding=\"async\" style=\"height: 29px; width: 315px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, x = 4, \u20134<\/p>\n<p style=\"text-align: justify;\">QR = <img decoding=\"async\" style=\"height: 23px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image056.png\" \/>, PR = <img decoding=\"async\" style=\"height: 25px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image059.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 7.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Find_a_relation_between_x_and_y_such_that_the_point_x_y_is_equidistant_from_the_point_3_6_and_%E2%80%933_4\"><\/span><strong>10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (\u20133, 4).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>It is given that (x, y) is equidistant from (3, 6) and (\u20133, 4).<\/p>\n<p style=\"text-align: justify;\">Using Distance formula, we can write<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 31px; width: 285px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 29px; width: 384px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image061.png\" \/><\/p>\n<p style=\"text-align: justify;\">Squaring both sides, we get<\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 24px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image062.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 24px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch07\/Ex7.1\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 \u22126x \u2212 12y + 45<\/p>\n<p style=\"text-align: justify;\">= 6x \u2212 8y + 25<\/p>\n<p style=\"text-align: justify;\">\u21d2 12x + 4y = 20<\/p>\n<p style=\"text-align: justify;\">\u21d2 3x + y = 5<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_71\"><\/span>NCERT Solutions for Class 10 Maths Exercise 7.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 Maths, Computer Science, Home Science,Hindi ,English, Social 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<strong><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\">the best app for CBSE\u00a0<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 7.1 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. 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