The rectangular coordinate system is also known as the
*Cartesian* coordinate system after Rene Descartes, who
popularized its use in analytic geometry. The rectangular coordinate system is
based on a grid, and every point on the plane can be identified by unique *x*
and *y* coordinates, just as any point on the Earth can be identified by
giving its latitude and longitude.

Locations on the grid are measured relative to a fixed point, called the *origin*,
and are measured according to the distance along a pair of axes. The *x*
and *y* axes are just like the number line, with positive distances to the
right and negative to the left in the case of the *x* axis, and positive distances
measured upwards and negative down for the *y* axis. Any displacement away
from the origin can be constructed by moving a specified distance in the *x*
direction and then another distance in the *y* direction. Think of it as
if you were giving directions to someone by saying something like “go three
blocks East and then 2 blocks North.”

We specify the location of a point by first giving its *x* coordinate
(the left or right displacement from the origin), and then the *y*
coordinate (the up or down displacement from the origin). Thus, every point on
the plane can be identified by a pair of numbers (*x*, *y*),
called its *coordinates*.

**Examples:**

Sometimes we just want to know what general part of the graph we are talking
about. The axes naturally divide the plane up into quarters. We call these *quadrants*,
and number them from one to four. Notice that the numbering begins in the upper
right quadrant and continues around in the counter-clockwise direction. Notice
also that each quadrant can be identified by the unique combination of positive
and negative signs for the coordinates of a point in that quadrant.