NCERT Solutions for Class 9th Maths Chapter 1 Orienting Yourself: The Use of Coordinates
Updated on 2026-09-19
About this chapter
Two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meet at the origin O (0, 0). Together they are the coordinate axes, and the plane they lie in is the Cartesian plane (also: coordinate plane, xy-plane). For a point P ( x , y ), x is the perpendicular distance of P from the y-axis measured along the x-axis, and y is its perpendicular distance from the x-axis measured along the y-axis. Right and up are positive; left and down are negative. Because each of the two displacements carries its own sign, there are 2 × 2 = 4 sign patterns, and so exactly four quadrants : I (+, +), II (−, +), III (−, −), IV (+, −). A point with a zero displacement sits on an axis and belongs to no quadrant: ( x , 0) on the x-axis, (0, y ) on the y-axis. The pair is ordered . ( x , y )
- Settling In
- The 2-d Cartesian Coordinate System
- After Exercise Set 1.1
- After Fig. 1.4
- Distance Between Two Points in the 2-D Plane
- Chapter 1 Orienting Yourself: The Use of Coordinates
Quick revision
| Idea | What it means | Coordinate form | Example from the chapter |
|---|---|---|---|
| Origin | The point where the two axes cross — the zero of both number lines | (0, 0) | O (0, 0) |
| x-coordinate | Signed perpendicular distance from the y-axis, counted along the x-axis | first entry of (x, y) | For D (7, 1), x = 7 |
| y-coordinate | Signed perpendicular distance from the x-axis, counted along the y-axis | second entry of (x, y) | For D (7, 1), y = 1 |
| Point on the x-axis | Zero distance from the x-axis | (x, 0) | B (4.5, 0) |
| Point on the y-axis | Zero distance from the y-axis | (0, y) | H (0, 4), G (0, −4.5) |
| Quadrant I | Right of the y-axis and above the x-axis | (+, +) | A (3, 4) |
| Quadrant II | Left of the y-axis and above the x-axis | (−, +) | Q (−5, 3) |
| Quadrant III | Left of the y-axis and below the x-axis | (−, −) | M (−3, −4) |
| Quadrant IV | Right of the y-axis and below the x-axis | (+, −) | S (3, −5) |
| Distance along a grid line | Only one coordinate changes | |x2 − x1| or |y2 − y1| | C (3, 1) to D (7, 1) is 4 units |
| Distance, any two points | The two shifts are the legs of a right triangle | √((x2−x1)² + (y2−y1)²) | A (3, 4) to D (7, 1) is 5 units |
| Midpoint | Each coordinate is the average of the two end coordinates | ((x1+x2)/2, (y1+y2)/2) | Midpoint of (−3, 0) and (3, 0) is (0, 0) |
Exercises
- In-text Questions — Settling In Page 3
- Exercise Set 1.1 — The 2-d Cartesian Coordinate System Page 5
- After Exercise Set 1.1 — Think and Reflect Page 5
- In-text Questions — The 2-d Cartesian Coordinate System Page 6
- In-text Questions — The 2-d Cartesian Coordinate System Page 7
- After Fig. 1.4 — Think and Reflect Page 7
- Exercise Set 1.2 — The 2-d Cartesian Coordinate System Page 8
- In-text Questions — Distance Between Two Points in the 2-D Plane Page 9
- Think and Reflect — Distance Between Two Points in the 2-D Plane Page 9
- In-text Questions — Distance Between Two Points in the 2-D Plane Page 11
- Think and Reflect — Distance Between Two Points in the 2-D Plane Page 11
- Chapter 1 Orienting Yourself: The Use of Coordinates — End-of-Chapter Exercises Page 12–14