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16 The Cartesian Coordinate Plane
In this chapter, you learn about the Cartesian coordinate plane.
Defi nitions for the Plane
The Cartesian coordinate plane is defi ned by two real number lines, one
horizontal and one vertical, intersecting at right angles at their zero points
(see Figure 16.1). The two real number lines are the coordinate axes. The
horizontal axis, commonly called the x-axis, has positive direction to the
right, and the vertical axis, commonly referred to as the y-axis, has positive
direction upward. The two axes determine a plane. Their point of intersec-
tion is called the origin.
Ordered Pairs in the Plane
In the (Cartesian) coordinate plane, you identify each point P in the plane
by an ordered pair (x, y) of real numbers x and y, called its coordinates. The
ordered pair (0, 0) names the origin. An ordered pair of numbers is written
in a defi nite order so that one number is fi rst and the other second. The fi rst
number is the x-coordinate, and the second number is the y-coordinate (see
Figure 16.2). The order in the ordered pair (xy) that corresponds to a point
P is important. The absolute value of the fi rst coordinate, x, is the perpen-
dicular horizontal distance (right or left) of the point P from the y-axis. If x
is positive, P is to the right of the y-axis; if x is negative, it is to the left of the
y-axis. The absolute value of the second coordinate, y, is the perpendicular
