Class 9 Maths Formula Sheet 2026-27

3.1 LOCATING A POINT IN A PLANE

To fix the position of a point on a straight line, one number is enough: its distance from a chosen starting point, with a sign to show on which side it lies. A point on a flat surface, however, cannot be described by a single number. If a student tells a friend over the phone that a table stands 'near the wall' of a room, the friend still cannot place it; what is needed is its distance from two walls that meet at a corner.

Mathematicians use the same idea. Two number lines are drawn at right angles to each other, one horizontal and one vertical, crossing at their zero points. The horizontal line is the x-axis, the vertical line is the y-axis, and the point where they cross is the origin O. A plane marked in this way is called the coordinate or Cartesian plane, after the French thinker René Descartes, although the idea of fixing places by two distances was used much earlier by astronomers and map-makers, including in ancient India.

The perpendicular distance of a point from the y-axis is its x-coordinate, or abscissa, and its distance from the x-axis is its y-coordinate, or ordinate. The pair is always written in the order (x, y). The two axes divide the plane into four parts called quadrants.