Coordinate Plane and Graphs

Ordered Pairs and Coordinates

Position of Points on a Number Line

On the number line, the two points

and

correspond to the numbers

and

, respectively.
The number corresponding to a point on a number line is called the coordinate of that point. If the coordinate of point

, it is written as

The point with a coordinate of

is called the origin, denoted as

, so

.
Using this notation, the coordinates of the two points

and

on the number line are written as

and

, respectively.

Coordinates of Points on a Coordinate Plane

Ordered Pairs

An ordered pair is a pairing of two numbers where the order is significant. For example,

is different from

because their order is different.

Using ordered pairs, we can represent the location of points on a plane.

When two perpendicular number lines intersect at a point

, we call the horizontal line the -axis and the vertical line the -axis. Together, these two axes are called the coordinate axes, and the intersection point

is called the origin. The plane defined by these axes is the coordinate plane.

Coordinates of a Point on the Coordinate Plane

For a point

on the coordinate plane, if perpendicular lines are drawn from

to the

-axis and

-axis, the points of intersection determine the numbers

and

. The ordered pair

is called the coordinate of point

, written as

Here,

is the -coordinate of

, and

is the -coordinate of

Quadrants of the Coordinate Plane

The coordinate plane is divided into four regions by the coordinate axes. These regions are called the quadrants and are numbered as follows:

1st Quadrant
2nd Quadrant
3rd Quadrant
4th Quadrant

Signs of Coordinates in Each Quadrant

	1st Quadrant	2nd Quadrant	3rd Quadrant	4th Quadrant
Sign of -coordinate
Sign of -coordinate