The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system. A point in two dimensional space (visualized below) is denoted as P = (x,y) where x represents the distance from the origin in the x-direction and y represents the distance from the origin in the y-direction. The point where the two axis meet is the origin and is represented by the point (0,0).

A point in one dimension only has one component: its distance from zero. This is visualized below.

In two dimensions the cartesian coordinate system describes where on a plane a point lies by using two components.

In three dimensional space a point has three components a x-component, y-component, and z-comonent: P = (x,y,z). For example, the coordinates of the point below is (3, 2, 3).

A common usage of the cartesian coordinate system is to visualize the input and output of a function.

A function takes input and produces output. The idea is a useful way to abstract away complexity and, especially in the age of computers, is a practical tool to solve problems.