Cartesian Coordinate System

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).

Dimension

One Dimension

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

Cartesian Coordinate System One Dimension

Two Dimensions

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

Cartesian Coordinate System Two Dimensions

Three Dimensions

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).

Cartesian Coordinate System Three Dimensions

Usage

A common usage of the cartesian coordinate system is to visualize the input and output of a function. For example, the graph of the cosine function can be visualized in the 2D Cartesian Coordinate System below.

Graph of the Cosine Function