CBSE Class 8 Mathematics – 22. Introduction of Coordinate Geometry (Notes)

Cartesian coordinates

The system of describing the position of points in space using perpendicular axis lines that meet at a point is called cartesian coordinate.

The horizontal line (axis) is called X-axis in figure XOX’ is X-axis.

The vertical line (axis) is called Y-axis in figure YOY’ is Y-axis.

The point of intersection of X-axis and Y-axis is called Origin.

Each point in the cartesian coordinate system is determined using its x and y coordinate and represented as (x, y).

The Origin is represented using O (0, 0).

Coordinates of a Point

To write the coordinates of a point we need an x – coordinate and a y-coordinate of a point.

x-coordinate tells how many units to move right or left. It is also called the Abscissa.

y-coordinate tells how many units to move up or down. It is also called the Ordinate.

While writing the coordinates of a point in the coordinate plane, the x – coordinate comes first, and then the y – coordinate. We place the coordinates in brackets.

Coordinates of the point of intersection of x-axis and y-axis is (0, 0). This is called Origin.

In the above figure-

OB = CA = x coordinate (Abscissa)

CO = AB = y coordinate (Ordinate).

We write the coordinate as (x, y).

Example

Plot the given points on the graph sheet.

(2, 3)

(-3, 1)

(-1.5, – 2.5)

Solution:

Remark: If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

Quadrants- The coordinate axis divide the plane of the graph paper into four regions they are called quadrants.

 

Region	Quadrant	Signs of coordinates
XOY	I	(+, +)
YOX’	II	(-, +)
X’OY’	III	(-, -)
Y’OX	IV	(+, -)