The Coordinate Plane


Definition: Coordinate plane is a two-dimensional number line where the vertical line is called the y-axis and the horizontal is called the x-axis. These lines are perpendicular and intersect at their zero points which is called the origin.


A point in a coordinate plane is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinates and the second to the y-coordinate.

The completeness property for points in the plane tells us two things

1. Exactly one point in the plane is named given the numbers of the ordered pair and

2. Exactly one ordered pair of numbers names a given point in the plane.

To graph a point one draws a dot at the coordinates that corresponds to the ordered pair

To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. There is your x-coordinate. And then do the same but following a horizontal line to find the y-coordinate.

Domain & Range:

A relation is a set of ordered pairs. The first coordinate i.e. the x-coordinate is called the domain and the second i.e. the y-coordinate is called the range. The domain contains values that correspond to the independent variable whereas the range contains values corresponding to the dependent variable.

The coordinate plane has similar elements to the grid shown above. It consists of a horizontal axis and a vertical axis, number lines that intersect at right angles.

Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point’s location along the x-axis  and along the y-axis.

In an ordered pair, such as (xy), the first value is called the x-coordinate and the second value is the y-coordinate. Note that the x-coordinate is listed before the y-coordinate. Since the origin has an x-coordinate of 0 and a y-coordinate of 0, its ordered pair is written (0, 0).