## Rectangular Coordinates

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.

### Axes

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.”

### Coordinates, Graphing Points

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:**

### Quadrants

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.