Angles lie in a plane. To specify the point in space where an angle lies, or where any figure exists, a plane can be assigned coordinates. Since a plane is two-dimensional, only two coordinates are required to designate a specific location for every point in the plane. One coordinate determines the length, and the other determines width. In reality, length and width are the same thing--they are used because they describe distance in two directions which are perpendicular to each other. This is all the coordinate plane is: a plane with two perpendicular axes by which distance in either of two dimensions can be measured.

The coordinate plane consists of an origin and two axes. The origin is a point. The axes are lines perpendicular to each other that intersect at the origin. Below is pictured the coordinate plane, with the origin at point O.

The origin is fixed, and designated as the point (0,0). Every other point is assigned an ordered pair, (x, y), according to its position relative to the origin. The two axes are named the \$x\$-axis and the y-axis. In most drawings, the x-axis is the horizontal axis, and the y-axis is the vertical axis, but this does not necessarily need to be the case. A point is assigned an ordered pair consisting of two real numbers: The first is the x-coordinate, which measures how far the point is from the y-axis. The second real number making up an ordered pair is the y-coordinate, which measures the distance between the point and the x-axis. Often the axes are pictured with tick marks indicating length to make it easier to measure distance. When a point is drawn into the coordinate plane and assigned an ordered pair, it is plotted. Take a gander at the plotted points below.