{"id":1809,"date":"2026-05-20T08:38:37","date_gmt":"2026-05-20T08:38:37","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1809"},"modified":"2026-06-20T12:28:37","modified_gmt":"2026-06-20T06:58:37","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":"NCERT Class 9 Maths End of Chapter Exercise Solutions | Coordinate Geometry"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-2910895535\"><div id=\"mymoc-1235249694\"><a href=\"https:\/\/amzn.to\/3S4CntS\" aria-label=\"Stationeries\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-300x89.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-1024x304.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-768x228.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div><div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">27<\/span><\/div>\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 &ndash; 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>&minus;<\/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>&minus;<\/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><\/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> A = (-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<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627-1024x683.png\" alt=\"\" class=\"wp-image-4915\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-627.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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 &ndash; 5. Can you predict the coordinates of point H which is on the line through W parallel to the y-axis? Which quadrants can H lie in?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628-1024x683.png\" alt=\"\" class=\"wp-image-4916\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-628.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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 the points R (3, 0), A (0, &ndash; 2), M (&ndash; 5, &ndash; 2) and P (&ndash; 5, 2). If<br>they are joined in the same order, predict:<br>(i) Two sides of RAMP that are perpendicular to each other.<br>(ii) One side of RAMP that is parallel to one of the axes.<br>(iii) Two points that are mirror images of each other in one axis.<br>Which axis will this be?<br>Now plot the points and verify your predictions<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"914\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-85-1024x914.png\" alt=\"image\" class=\"wp-image-3087\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-85-1024x914.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-85-300x268.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-85-768x686.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-85.png 1327w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\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 point Z (5, &ndash; 6) on the Cartesian plane. Construct a right-angled<br>triangle IZN and find the lengths of the three sides.<br>(Comment: Answers may differ from person to person.)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-86-1024x819.png\" alt=\"image\" class=\"wp-image-3088\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-86-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-86-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-86-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-86.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Comment: Answers May Differ from Person to Person<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This question gives only one point, <strong>Z(5, &ndash;6)<\/strong>. The positions of points <strong>I<\/strong> and <strong>N<\/strong> are not fixed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, different students may choose different points <strong>I<\/strong> and <strong>N<\/strong> to construct a right-angled triangle <strong>IZN<\/strong> with <strong>Z<\/strong> as one of its vertices.<\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-1-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\">As a result:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The shape and size of the triangle may vary.<\/li>\n\n\n\n<li>The lengths of the sides may be different.<\/li>\n\n\n\n<li>More than one correct answer is possible.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The only requirement is that <strong>IZN must be a right-angled triangle<\/strong> and <strong>Z(5, &ndash;6)<\/strong> must be one of its vertices.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Hence, the note &ldquo;Answers may differ from person to person&rdquo; means that different valid constructions can lead to different side lengths, and all such answers are acceptable if the triangle is right-angled.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\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 would a system of coordinates be like if we did not have<br>negative numbers? Would this system allow us to locate all the<br>points on a 2-D plane?<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-87-1024x819.png\" alt=\"image\" class=\"wp-image-3091\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-87-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-87-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-87-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-87.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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 the points M (&ndash; 3, &ndash; 4), A (0, 0) and G (6, 8) on the same straight<br>line? Suggest a method to check this without plotting and joining<br>the points.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-88-1024x819.png\" alt=\"image\" class=\"wp-image-3092\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-88-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-88-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-88-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-88.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">Use your method (from Problem 6) to check if the points<br>R (&ndash; 5, &ndash; 1), B (&ndash; 2, &ndash; 5) and C (4, &ndash; 12) are on the same straight line.<br>Now plot both sets of points and check your answers.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-89-1024x819.png\" alt=\"image\" class=\"wp-image-3093\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-89-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-89-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-89-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-89.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">Using the origin as one vertex, plot the vertices of:<br>(i) A right-angled isosceles triangle.<br>(ii) An isosceles triangle with one vertex in Quadrant III and the other in Quadrant IV<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-90-1024x819.png\" alt=\"image\" class=\"wp-image-3094\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-90-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-90-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-90-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-90.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">The following table shows the coordinates of points S, M and T. In each case, state whether M is the midpoint of segment ST. Justify your answer.<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"693\" height=\"244\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-94.png\" alt=\"image\" class=\"wp-image-3100\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-94.png 693w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-94-300x106.png 300w\" sizes=\"(max-width: 693px) 100vw, 693px\"><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When M is the mid-point of ST, can you find any connection between the coordinates of M, S and T?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"615\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96-1024x615.png\" alt=\"image\" class=\"wp-image-3102\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96-1024x615.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96-300x180.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96-768x461.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96-1536x922.png 1536w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-96.png 1619w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/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\">Use the connection you found to find the coordinates of B given<br>that M (&ndash;7, 1) is the midpoint of A (3, &ndash;&#8202;4) and B (x, y).<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-97-1024x683.png\" alt=\"image\" class=\"wp-image-3103\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-97-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-97-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-97-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-97.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">Let P, Q be points of trisection of AB, with P closer to A, and Q closer to B. Using your knowledge of how to find the coordinates of the midpoint of a segment, how would you find the coordinates of P and Q? Do this for the case when the points are A (4, 7) and B (16, &ndash;2).<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-98-819x1024.png\" alt=\"image\" class=\"wp-image-3106\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-98-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-98-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-98-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-98.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\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\">(i) Given the points A (1, &ndash;&#8202;8), B (&ndash;&#8202;4, 7) and C (&ndash;7, &ndash;&#8202;4), show that they lie on a circle K whose center is the origin O (0, 0). What is the radius of circle K?<br>(ii) Given the points D (&ndash;&#8202;5, 6) and E (0, 9), check whether D and E<br>lie within the circle, on the circle, or outside the circle K.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"882\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-99-882x1024.png\" alt=\"image\" class=\"wp-image-3107\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-99-882x1024.png 882w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-99-258x300.png 258w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-99-768x891.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-99.png 1164w\" sizes=\"(max-width: 882px) 100vw, 882px\"><\/figure>\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\">The midpoints of the sides of triangle ABC are the points D, E, and F. Given that the coordinates of D, E, and F are (5, 1), (6, 5), and (0, 3), respectively, find the coordinates of A, B and C.<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-100-1024x683.png\" alt=\"image\" class=\"wp-image-3110\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-100-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-100-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-100-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-100.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">A city has two main roads which cross each other at the centre of the city. These two roads are along the North&ndash;South (N&ndash;S) direction and East&ndash;West (E&ndash;W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction.<br>(i) Using 1 cm = 200 m, draw a model of the city in your notebook. Represent the roads\/streets by single lines.<br>(ii) There are street intersections in the model. Each street intersection is formed by two streets&thinsp;&mdash;&thinsp;one running in the N&ndash;S direction and another in the E&ndash;W direction. Each street intersection is referred to in the following manner: If the second street running in the N&ndash;S direction and 5th street in the E&ndash;W direction meet at some crossing, then we call this street intersection (2, 5). Using this convention, find:<br>(a) how many street intersections can be referred to as (4, 3).<br>(b) how many street intersections can be referred to as (3, 4)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-101-1024x683.png\" alt=\"image\" class=\"wp-image-3111\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-101-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-101-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-101-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-101.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\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\">A computer graphics program displays images on a rectangular screen whose coordinate system has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150). Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230). Determine:<br>(i) whether any part of either circle lies outside the screen.<br>(ii) whether the two circles intersect each other<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-102-1024x683.png\" alt=\"image\" class=\"wp-image-3112\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-102-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-102-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-102-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-102.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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\">Plot the points A (2, 1), B (&ndash;1, 2), C (&ndash;2, &ndash;1), and D (1, &ndash;2) in the coordinate plane. Is ABCD a square? Can you explain why? What is the area of this square?<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-103-1024x683.png\" alt=\"image\" class=\"wp-image-3113\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-103-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-103-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-103-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/image-103.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\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<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-2-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><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 (&minus;3, 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><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-4235347293\"><div id=\"mymoc-3109058754\"><a href=\"https:\/\/amzn.to\/4v5gV6P\" aria-label=\"calculators\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png 1302w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-300x99.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-1024x338.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-768x254.png 768w\" sizes=\"(max-width: 1302px) 100vw, 1302px\" width=\"1302\" height=\"430\"><\/a><\/div><\/div>\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<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/ncert-class-9-maths-exercise-2-1-solutions-introduction-to-linear-polynomials\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 2.1 Solutions &ndash; Introduction to Linear Polynomials<\/span><\/a><\/div><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> A = (-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<p class=\"wp-block-paragraph\">&#128216; Improve Your Maths Preparation with MyMockMate!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; Practice Chapter-wise Mock Tests<br>&#9989; Solve Important MCQs<br>&#9989; Download Notes PDF<br>&#9989; Get Instant Performance Analysis<br>&#9989; 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<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">27<\/span><\/div><div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-1743946602\"><div id=\"mymoc-877227257\"><a href=\"https:\/\/amzn.to\/4ehRB6n\" aria-label=\"printers\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-300x73.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-1024x250.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-768x187.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"318\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 27 Short Intro In this post, students can find complete step-by-step solutions for Class 9 Maths Chapter 1 End-of-Chapter Exercises &ndash; Coordinate Geometry. All&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1810,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[4,11],"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","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"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/05\/Class-9-Maths-End-of-Chapter-Exercise-Solutions-Coordinate-Geometry-NCERT-Solutions.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_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":7,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809\/revisions"}],"predecessor-version":[{"id":4917,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1809\/revisions\/4917"}],"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}]}}