Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional ( 3D ) space. The scheme gets its name from one of the first people known to have used it, the French mathematician and philosopher René Descartes (1596-1650). The Cartesian coordinate system is used to define positions on computer displays and in virtual reality (VR) renderings. The system is also employed in mathematics, physics, engineering, navigation, robotics , economics, and other sciences.

The Cartesian plane consists of two perpendicular axes that cross at a central point called the origin. Positions or coordinates are determined according to the *east/west* and *north/south* displacements from the origin. The east/west axis is often called the *x* axis, and the north/south axis is called the *y* axis. For this reason, the Cartesian plane is also known as the *xy* -plane. The *x* and *y* axes are linear number lines, meaning that each division on a given axis always represents the same increment. However, the increments on different axes can differ. For example, in the illustration at left below, each increment on the *x* axis might represent 2 units, while each increment on the *y* axis represents 5 units. Points or coordinates are indicated by writing an opening parenthesis, the *x* value, a comma, the *y* value, and a closing parenthesis in that order. An example is ( *x,y* ) = (2,-5). The origin is usually, but not always, assigned the value (0,0).

Cartesian three-space, also called *xyz* -space, has a third axis, oriented at right angles to the *xy* -plane. This axis, usually called the *z* axis, passes through the origin of the *xy* -plane. Positions or coordinates are determined according to the east/west ( *x* ), north/south ( *y* ), and *up/down* ( *z* ) displacements from the origin. As is the case with the *x* and *y* axes, the *z* axis is a linear number line. For example, in the illustration at right above, each increment on the *x* axis might represent 5 units, each increment on the *y* axis 10 units, and each increment on the *z* axis 2 units. Points or coordinates are indicated by writing an opening parenthesis, the *x* value, a comma, the *y* value, another comma, the *z* value, and a closing parenthesis in that order. An example is ( *x,y,z* ) = (5,-10,-4). The origin is usually, but not always, assigned the value (0,0,0).

*This was last updated in*March 2011

*Posted by:*Margaret Rouse

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