# The Cartesian Plane

An **ordered pair **(x, y) of real numbers has x as its first member and y as its second
member. The model for representing ordered pairs is called the **rectangular
coordinate system**, or the **Cartesian plane**, after the French mathematician RenÃ©
Descartes. It is developed by considering two real lines intersecting at right angles
(see the figure below).

The horizontal real line is usually called the **x-axis**, and the vertical real line is
usually called the **y-axis**. Their point of intersection is the **origin**. The two axes divide
the plane into four **quadrants**.

Each point in the plane (x, y) is identified by an ordered pair of real numbers x
and y, called **coordinates** of the point. The number x represents the directed distance
from the y-axis to the point, and the number y represents the directed distance from
the x-axis to the point. For the point (x, y), the first coordinate is the
x-coordinate or **abscissa**, and the second coordinate is the y-coordinate or
**ordinate**.
For example, the figure below shows the locations of the points (-1, 2), (3, 4),
(0, 0), (3, 0)
and (-2, -3) in the Cartesian plane.

**NOTE **The signs of the coordinates of a point determine the quadrant in which the point lies.
For instance, if x > 0 and y < 0, then (x, y) lies in Quadrant IV.

Note that an ordered pair (a, b) is used to denote either a point in the plane or an
open interval on the real line. This, however, should not be confusingâ€”the nature of
the problem should clarify whether a point in the plane or an open interval is being
discussed.