Download Orienting Yourself: The Use of Coordinates – NCERT Class 9 Maths Chapter 1 PDF from the new NCERT Class 9 Maths book Ganita Manjari (2026-27). Read the chapter online or download the free PDF. 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).
Orienting Yourself: The Use of Coordinates PDF – Chapter 1 of Ganita Manjari (Part I)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 1 PDF | Orienting Yourself: The Use of Coordinates | View PDF |
| Full book | NCERT Class 9 Maths – Ganita Manjari | View Book |
Read Online
What Is in Orienting Yourself: The Use of Coordinates? (Class 9 Maths Chapter 1)
- 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) = (y, x) only when x = y; otherwise the two are different points, mirror images of each other in the line through O that bisects Quadrants I and III.
- Distances along a grid line are differences: |x2 − x1| for a horizontal segment, |y2 − y1| for a vertical one.
- For any two points, the horizontal and vertical shifts are the legs of a right triangle, so by the Baudhāyana–Pythagoras Theorem the distance is √((x2 − x1)² + (y2 − y1)²). Squaring removes the signs, so it does not matter which point is called first.
Quick revision – Orienting Yourself: The Use of Coordinates
| 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) |
Old NCERT vs New – Class 9 Maths
This chapter is from Ganita Manjari, the new NCERT Class 9 Maths book (NCF-SE 2023, used from 2026-27). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Manjari:
Orienting Yourself: The Use of Coordinates – Overview
| Class | Class 9 |
| Subject | Maths |
| Book | Ganita Manjari – new NCERT book |
| Part | Part I |
| Chapter | 1 of 14 – Orienting Yourself: The Use of Coordinates |
| Book pages | 1 – 15 |
| Edition | Latest NCERT edition (2026-27) |
| Session | 2026-27 |
| Free – read online or download |
Class 9 Maths Chapter 1 – FAQs
Where can I download Orienting Yourself: The Use of Coordinates Class 9 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 9 Maths Chapter 1 about?
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).
Is Orienting Yourself: The Use of Coordinates from the new NCERT Class 9 Maths book?
Yes. It is chapter 1 of ganita manjari (part i), the new NCERT Class 9 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 9 Maths Chapter 1?
Open the NCERT Solutions link above for answers to the exercise questions.