## Class 9th Maths Chapter 3 Coordinate Geometry Notes

__Cartesian System__

Cartesian plane & Coordinate Axes

**Cartesian Plane**: A cartesian plane is defined by **two perpendicular number lines**, A horizontal line(x−axis) and a vertical line (y−axis).

These lines are called coordinate axes. The Cartesian plane extends infinitely in all directions.

**Origin**: The coordinate axes intersect each other at right angles, **The point of intersection** of these two axes is called Origin.

**Quadrants**

The cartesian plane is divided into four equal parts, called **quadrants. **These are named in the order as I,II,III and IV starting with the upper right and going around in anticlockwise direction.

Points in different Quadrants.

Signs of coordinates of points in different quadrants:

**I Quadrant:** ‘+’ x – coordinate and ‘+’ y – coordinate. E.g. (2,3)

**II Quadrant: **‘-’ x – coordinate and ‘+’ y – coordinate. E.g. (-1,4)

**III Quadrant: **‘-’ x – coordinate and ‘-’ y – coordinate. E.g. (-3,-5)

**IV Quadrant: **‘+’ x – coordinate and ‘-’ y – coordinate. E.g. (6,-1)

Plotting on a Graph

Representation of a point on the Cartesian plane

Using the co-ordinate axes, we can describe any point in the plane using an ordered pair of numbers. A point **A **is represented by an ordered pair (x,y) where x is the **abscissa** and y is the **ordinate** of the point.

Position of a point in a plane

Plotting a point

The coordinate points will define the location in the cartesian plane. The first point (x) in the coordinates represents the horizontal axis and the second point in the coordinates (y) represent the vertical axis.

Consider an example, Point (3,2) is 3 units away from the positive y-axis and 2 units away from the positive x-axis. Therefore, point (3,2) can be plotted as shown below. Similarly, (-2,3), (-1,-2) and (2,-3) are plotted.

Plotting a point in the plane