{"id":1809,"date":"2026-05-20T08:38:37","date_gmt":"2026-05-20T08:38:37","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1809"},"modified":"2026-05-20T08:46:33","modified_gmt":"2026-05-20T08:46:33","slug":"class-9-maths-end-of-chapter-exercise-solutions-coordinate-geometry-ncert-solutions","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/class-9-maths-end-of-chapter-exercise-solutions-coordinate-geometry-ncert-solutions\/","title":{"rendered":"Class 9 Maths End of Chapter Exercise Solutions | Coordinate Geometry NCERT Solutions"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">In this post, students can find complete step-by-step solutions for Class 9 Maths Chapter 1 End-of-Chapter Exercises \u2013 Coordinate Geometry. All questions are solved in simple and exam-oriented language based on the latest NCERT syllabus. This chapter helps students understand coordinates, quadrants, plotting points, midpoint concepts, and distance between points in the Cartesian plane.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Item<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Board<\/td><td>NCERT \/ CBSE<\/td><\/tr><tr><td>Class<\/td><td>9<\/td><\/tr><tr><td>Subject<\/td><td>Maths<\/td><\/tr><tr><td>Chapter<\/td><td>Coordinate Geometry<\/td><\/tr><tr><td>Exercise Type<\/td><td>End-of-Chapter Exercise<\/td><\/tr><tr><td>Main Topics<\/td><td>Coordinates, Distance, Midpoint<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cartesian Plane<\/li>\n\n\n\n<li>Coordinates of Points<\/li>\n\n\n\n<li>Quadrants<\/li>\n\n\n\n<li>Distance Formula<\/li>\n\n\n\n<li>Midpoint Formula<\/li>\n\n\n\n<li>Reflection in Axes<\/li>\n\n\n\n<li>Collinearity of Points<\/li>\n\n\n\n<li>Coordinate Geometry Applications<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter introduces the coordinate plane, quadrants, and methods to locate and measure distances between points.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Distance Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><mo stretchy=\"false\">(<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>y<\/mi><mn>1<\/mn><\/msub><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}<\/annotation><\/semantics><\/math>(x2\u200b\u2212x1\u200b)2+(y2\u200b\u2212y1\u200b)2\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Midpoint Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mrow><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2}\\right)<\/annotation><\/semantics><\/math>(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)-10-8-6-4-2246810-2246810A = (-6, -1)B = (6, 7)M = (0, 3)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Coordinates of Origin<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(0, 0)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What are the x-coordinate and y-coordinate of the point of intersection of the two axes?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The x-axis and y-axis intersect at the origin.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Coordinates = (0, 0)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Point W has x-coordinate equal to \u22125. Predict coordinates of H on line parallel to y-axis.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If H lies on a line parallel to the y-axis through W, then:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x-coordinate of H = \u22125<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Possible coordinates:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u22125, y)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">H may lie in:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quadrant II<\/li>\n\n\n\n<li>Quadrant III<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">depending on value of y.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Consider points R (3, 0), A (0, \u22122), M (\u22125, \u22122) and P (\u22125, 2).<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Perpendicular sides<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>RA \u27c2 AM<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Side parallel to axis<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>AM is parallel to x-axis<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(iii) Mirror image points<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code>A (0, \u22122) and P (\u22125, 2)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">are reflected across x-axis.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Plot Z (5, \u22126) and construct triangle.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using origin O:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distance OZ:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>6<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mn>61<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{5^2+(-6)^2}=\\sqrt{61}<\/annotation><\/semantics><\/math>52+(\u22126)2\u200b=61\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sides:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Base = 5 units<br>Height = 6 units<br>Hypotenuse = \u221a61 units<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What if negative numbers did not exist?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Without negative numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Only first quadrant would exist.<\/li>\n\n\n\n<li>We could not locate points left or below origin.<\/li>\n\n\n\n<li>Complete coordinate geometry would not be possible.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Are M (\u22123, \u22124), A (0, 0), and G (6, 8) collinear?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Distance MA:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>3<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{(-3)^2+(-4)^2}=5<\/annotation><\/semantics><\/math>(\u22123)2+(\u22124)2\u200b=5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distance AG:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>8<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{6^2+8^2}=10<\/annotation><\/semantics><\/math>62+82\u200b=10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distance MG:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><msup><mn>9<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>12<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{9^2+12^2}=15<\/annotation><\/semantics><\/math>92+122\u200b=15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>MA + AG = MG<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Points are collinear.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Check whether R (\u22125, \u22121), B (\u22122, \u22125), C (4, \u221212) are collinear.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using distance formula:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>RB = 5<br>BC = \u221a85<br>RC = \u221a130<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>RB + BC \u2260 RC<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Points are not collinear.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 8<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Plot triangles using origin.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Right-angled isosceles triangle<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Possible vertices:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>O(0,0), A(4,0), B(0,4)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Isosceles triangle in Quadrant III and IV<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Possible vertices:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A(\u22124,\u22122), B(4,\u22122), O(0,0)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 9<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Check midpoint cases.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Midpoint formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mrow><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2}\\right)<\/annotation><\/semantics><\/math>(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)-10-8-6-4-2246810-2246810A = (-6, -1)B = (6, 7)M = (0, 3)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answers<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>S<\/th><th>M<\/th><th>T<\/th><th>Midpoint?<\/th><\/tr><\/thead><tbody><tr><td>(\u22123,0)<\/td><td>(0,0)<\/td><td>(3,0)<\/td><td>Yes<\/td><\/tr><tr><td>(2,3)<\/td><td>(3,4)<\/td><td>(4,5)<\/td><td>Yes<\/td><\/tr><tr><td>(0,0)<\/td><td>(0,5)<\/td><td>(0,\u221210)<\/td><td>No<\/td><\/tr><tr><td>(\u22128,7)<\/td><td>(0,\u22122)<\/td><td>(6,\u22123)<\/td><td>No<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 10<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Find coordinates of B.<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>M(\u22127,1)<br>A(3,\u22124)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using midpoint formula:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(3 + x)\/2 = \u22127<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>x = \u221217<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>(\u22124 + y)\/2 = 1<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>y = 6<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B = (\u221217, 6)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 11<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Coordinates of trisection points.<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A(4,7), B(16,\u22122)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Using section division:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>P = (8,4)<br>Q = (12,1)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 12<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Circle centered at origin.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Distance OA:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><msup><mn>1<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>8<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mn>65<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{1^2+(-8)^2}=\\sqrt{65}<\/annotation><\/semantics><\/math>12+(\u22128)2\u200b=65\u200b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>OB = \u221a65<br>OC = \u221a65<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>All points lie on same circle.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Radius:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u221a65 units<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 13<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Find coordinates of A, B and C.<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Using midpoint relations:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>A = (11,3)<br>B = (1,\u22121)<br>C = (\u22121,7)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 14<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">City roads model.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Draw coordinate grid using:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>1 cm = 200 m<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">(a)<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Only 1 intersection can be (4,3)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">(b)<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Only 1 intersection can be (3,4)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 15<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Computer graphics circles.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Circle A:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>No part lies outside screen.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Circle B:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>No part lies outside screen.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Distance between centers:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msqrt><mrow><mo stretchy=\"false\">(<\/mo><mn>250<\/mn><mo>\u2212<\/mo><mn>100<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>230<\/mn><mo>\u2212<\/mo><mn>150<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{(250-100)^2+(230-150)^2}<\/annotation><\/semantics><\/math>(250\u2212100)2+(230\u2212150)2\u200b<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\u2248 170 units<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Since:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>80 + 100 &gt; 170<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Circles intersect.<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Question 16<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Is ABCD a square?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Using distance formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">All sides are equal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diagonals are perpendicular.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ABCD is a square.<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Area:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Side\u00b2 = 10 square units<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Writing coordinates in wrong order<\/li>\n\n\n\n<li>Forgetting negative signs<\/li>\n\n\n\n<li>Incorrect midpoint calculations<\/li>\n\n\n\n<li>Mistakes in distance formula<\/li>\n\n\n\n<li>Wrong quadrant identification<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Learn quadrant signs carefully.<\/li>\n\n\n\n<li>Practice graph plotting daily.<\/li>\n\n\n\n<li>Always simplify square roots properly.<\/li>\n\n\n\n<li>Use graph paper neatly.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Coordinates of origin are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. (1,0)<br>B. (0,1)<br>C. (0,0)<br>D. (1,1)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. (0,0)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Point (\u22123, 5) lies in:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Quadrant I<br>B. Quadrant II<br>C. Quadrant III<br>D. Quadrant IV<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. Quadrant II<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Distance between points is found using:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Midpoint Formula<br>B. Distance Formula<br>C. Area Formula<br>D. Ratio Formula<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. Distance Formula<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What is the Cartesian plane?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The plane formed by x-axis and y-axis is called Cartesian plane.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What are coordinates of origin?<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>(0, 0)<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">What is midpoint formula?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo fence=\"true\">(<\/mo><mfrac><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo separator=\"true\">,<\/mo><mfrac><mrow><msub><mi>y<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>y<\/mi><mn>2<\/mn><\/msub><\/mrow><mn>2<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\frac{x_1+x_2}{2},\\frac{y_1+y_2}{2}\\right)<\/annotation><\/semantics><\/math>(2&#215;1\u200b+x2\u200b\u200b,2y1\u200b+y2\u200b\u200b)-10-8-6-4-2246810-2246810A = (-6, -1)B = (6, 7)M = (0, 3)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Why is Coordinate Geometry important?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">It is used in mathematics, engineering, maps, graphics, and navigation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">CTA (Call To Action)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udcd8 Improve Your Maths Preparation with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2705 Practice Chapter-wise Mock Tests<br>\u2705 Solve Important MCQs<br>\u2705 Download Notes PDF<br>\u2705 Get Instant Performance Analysis<br>\u2705 Prepare Smarter for Board Exams<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start learning now on <a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.mymockmate.com?utm_source=chatgpt.com\">MyMockMate<\/a><\/p>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p>Short Intro In this post, students can find complete step-by-step solutions for Class 9 Maths Chapter 1 End-of-Chapter<\/p>\n","protected":false},"author":1,"featured_media":1810,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"page_builder":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,11,127],"tags":[141,139,136,165,172,169,137,140,171,161,160,144,166,154,167,157,163,89,164,168,53,47,149,155,170],"class_list":["post-1809","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","category-maths-class-9","category-orienting-yourself-the-use-of-coordinates","tag-cartesian-plane","tag-cbse-class-9-maths","tag-class-9-maths","tag-class-9-maths-chapter-1-solutions","tag-class-9-ncert-solutions","tag-collinear-points","tag-coordinate-geometry","tag-coordinate-geometry-chapter-1","tag-coordinate-geometry-exercise-solutions","tag-coordinate-geometry-mcqs","tag-coordinate-geometry-notes","tag-coordinate-geometry-questions-answers","tag-coordinate-plane","tag-coordinates-of-points","tag-distance-between-two-points","tag-distance-formula","tag-end-of-chapter-exercise-solutions","tag-maths-board-exam-preparation","tag-midpoint-formula","tag-midpoint-questions","tag-ncert-maths-solutions","tag-ncert-solutions","tag-plotting-points","tag-quadrants","tag-reflection-in-coordinate-geometry"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=1809"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809\/revisions"}],"predecessor-version":[{"id":1811,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809\/revisions\/1811"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1810"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}