Chapter 1 — Orienting Yourself: The Use of Coordinates

Chapter 1 of the Class 9 Maths NCERT textbook (Mathematics), "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.

• History of coordinates — Traces grid-based thinking from the Sindhu-Sarasvati Civilisation and Baudhayana through Brahmagupta to Descartes and Fermat, showing how the idea of locating points by numbers developed over millennia.
• The Cartesian plane — Two perpendicular axes — the x-axis and y-axis — meet at the origin O (0, 0) and divide the plane into four quadrants, so any point in the plane can be named by an ordered pair (x, y).
• Plotting and identifying points — A point's sign pattern fixes which quadrant it lies in, letting students both plot a point from its coordinates and read a point's coordinates off a graph.
• Distance between two points — The Baudhayana-Pythagoras Theorem gives the straight-line distance between any two plotted points, linking the coordinate system to measurement.

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)