


The Coordinate Plane
The coordinate plane is a plane determined by two perpendicular
lines, the xaxis and the yaxis.
The xaxis is the horizontal axis, and the yaxis
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 yaxes 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 xcoordinate.
The xcoordinate of a point is its location along
the xaxis and can be determined by the point’s distance
from the yaxis (where x = 0).
If the point is to the right of the yaxis, its xcoordinate
is positive, and if the point is to the left of the yaxis,
its xcoordinate is negative. The second coordinate
in a coordinate pair is the ycoordinate. The ycoordinate
of a point is its location along the yaxis and
can be calculated as the distance from that point to the xaxis.
If the point is above the xaxis, its ycoordinate
is positive, and if the point is below the xaxis,
its ycoordinate is negative.
The Quadrants
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 xcoordinate 4 units to the right of the yaxis
and a ycoordinate 2 units below the xaxis.
This is how the coordinates of a point specify its exact location.
The coordinates of the origin are, by definition, (0, 0).
