The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.

Three-dimensional Cartesian Coordinate System

The three-dimensional Cartesian coordinate is defined by three axes at right angles to each other, forming a three dimensional space. The three axes are labeled x (sometimes called abscissa), y (ordinate), and z (applicate). The point of intersection, where the axes meet, is called the origin, which is normally labeled O.

To specify a particular point on a three dimensional coordinate system, you indicate the particular values on the axes in the form [x,y,z].

Two points in the 3D cartesian coordinate system.

The distance between a point P and the origin O calculates from the Pythagorean theorem:

The shortest distance between two points P1 and P2 calculates the same way as:

Last Update: 2010-12-06