Definition:Cartesian Coordinate System

2 Dimensions


The points in the plane can be identified uniquely by means of a pair of coordinates.

Two perpendicular straight lines are chosen. These are understood to be infinite. These are called the axes.

The usual directions to make these are:
 * Across the page, from left to right. This is usually called the x-axis.
 * Up the page, from bottom to top. This is usually called the y-axis.

The point of intersection of the axes is called the origin.

A unit length is specified.

The axes are each identified with the set of real numbers $$\mathbb{R}$$, where the origin is identified with $$0$$.

The real numbers increase to the right on the x-axis, upwards on the y-axis.

Any point on the plane is now able to be identified by means of a pair of coordinates $$\left({x, y}\right)$$, as follows:

Quadrants
For ease of reference, the coordinate plane is often divided into four regions by the axes:
 * The area above the x-axis and to the right of the y-axis is called the first quadrant
 * The area above the x-axis and to the left of the y-axis is called the second quadrant
 * The area below the x-axis and to the left of the y-axis is called the third quadrant
 * The area below the x-axis and to the right of the y-axis is called the fourth quadrant

Note that the axes are generally not considered to belong to any quadrant.