Chapter 1 — Orienting Yourself: The Use of Coordinates

Chapter 1 of NCERT Class 9 Maths, "Orienting Yourself: The Use of Coordinates", introduces the 2-D Cartesian coordinate system, showing how any point in a plane is located using an ordered pair (x, y) measured from two perpendicular axes, and how to find the distance between two points.

This chapter opens with the rich history of grid-based thinking and coordinates, from the Sindhu-Sarasvati Civilisation and Baudhayana to Brahmagupta, Descartes and Fermat. Through the story of Reiaan and Shalini, it builds the 2-D Cartesian coordinate system: the x-axis, y-axis, the origin O (0, 0), and the four quadrants. Students learn to write a point as (x, y), identify which quadrant a point lies in by its sign pattern, plot points on a graph, and find the distance between two points using the Baudhayana-Pythagoras Theorem. It closes with a chapter summary and end-of-chapter exercises.

1. 01The 2-D system uses two perpendicular lines: horizontal x-axis and vertical y-axis
2. 02The origin O is where the axes meet; its coordinates are (0, 0)
3. 03Axes divide the plane into four quadrants with sign patterns (+,+), (-,+), (-,-), (+,-)
4. 04x-coordinate is distance from the y-axis; y-coordinate is distance from the x-axis
5. 05Points on the x-axis are (x, 0); points on the y-axis are (0, y)
6. 06Distance between (x1, y1) and (x2, y2) is sqrt((x2-x1)^2 + (y2-y1)^2)
7. 07If x = y then (x, y) = (y, x); if x != y then (x, y) != (y, x)