Class 9 Mathematics NCERT Ganita Manjari Chapter 1
Orienting Yourself: The Use of Coordinates

Coordinate Geometry is a branch of Mathematics that uses coordinates to locate points and study geometric figures on a coordinate plane.

A coordinate plane is a flat surface formed by the X-axis and Y-axis. It is used to locate and represent points using ordered pairs.

An ordered pair is a pair of numbers written as (x, y), where x represents the horizontal position and y represents the vertical position of a point.

The origin is the point (0, 0) where the X-axis and Y-axis intersect.

The X-axis is the horizontal number line on the coordinate plane.

The Y-axis is the vertical number line on the coordinate plane.

There are four quadrants. They are numbered I, II, III, and IV in the anticlockwise direction.

Quadrant I: (+, +)
Quadrant II: (−, +)
Quadrant III: (−, −)
Quadrant IV: (+, −)

The distance between two points is found using the distance formula:

d = √[(x₂ − x₁)² + (y₂ − y₁)²]

Symmetry means reflecting a point or figure about the X-axis, Y-axis, or the origin while maintaining equal distance from the line of reflection.

Only the y-coordinate changes its sign.
Example: (4, 3) → (4, −3)

Only the x-coordinate changes its sign.
Example: (4, 3) → (−4, 3)

Yes. A point with y = 0 lies on the X-axis, and a point with x = 0 lies on the Y-axis.

The order is important because (x, y) and (y, x) represent different points on the coordinate plane.

Coordinate geometry is used in GPS navigation, Google Maps, computer graphics, architecture, engineering, robotics, astronomy, surveying, medical imaging, and video game development.