The Coordinate Plane
The coordinate plane is a plane determined by two perpendicular
lines, the x-axis and the y-axis.
The x-axis is the horizontal axis, and the y-axis
is the vertical axis. Any other point in the plane can be stated
by a pair of coordinates that express the location of the point
in terms of the two axes. The intersection of the x-
and y-axes is designated as the origin and is the
point (0, 0). Following is a figure of the coordinate
plane with a few points labeled with their coordinates:
As you can see from the figure, each of the points on
the coordinate plane receives a pair of coordinates: (x, y).
The first coordinate in a coordinate pair is called the x-coordinate.
The x-coordinate of a point is its location along
the x-axis and can be determined by the point’s distance
from the y-axis (where x = 0).
If the point is to the right of the y-axis, its x-coordinate
is positive, and if the point is to the left of the y-axis,
its x-coordinate is negative. The second coordinate
in a coordinate pair is the y-coordinate. The y-coordinate
of a point is its location along the y-axis and
can be calculated as the distance from that point to the x-axis.
If the point is above the x-axis, its y-coordinate
is positive, and if the point is below the x-axis,
its y-coordinate is negative.
The coordinate plane is divided into four quadrants. Each
quadrant is a specific region in the coordinate plane. The region
in which x > 0 and y > 0 is Quadrant
I. The region in which x < 0 and y >
0 is Quadrant II. The region in which x < 0
and y < 0 is Quadrant III. The region in which x >
0 and y < 0 is Quadrant IV.
For example, the point (4, –2) lies in Quadrant IV, with
an x-coordinate 4 units to the right of the y-axis
and a y-coordinate 2 units below the x-axis.
This is how the coordinates of a point specify its exact location.
The coordinates of the origin are, by definition, (0, 0).