Cartesian Coordinates. XYZ axes. This animation shows how Cartesian coordinates can describe a point along a line, in a plane, or in a space. The video begins with a square sheet of paper that develops a grid pattern of fine blue lines. A central red point (origin) appears. Then X and Y axes emerge (positive are brass coloured, negative are dark red). The positions +10 and -10 are indicated along the number lines. A point (purple) moves to position 7 along the X axis, and then to position 5 on the Y axis. These coordinates are written as (7,5). Then a blue point moves to position -5 on the X axis, and then to -9 on the Y axis, so its coordinates are (-5,-9). Up until now, everything has happened in the plane of the sheet of paper. In fact, you can do all of this with a real piece of paper on a desk. Then the purple point moves upwards, above of the piece of paper, and the vertical (Z) axis emerges. The point stops at 8 units above the paper (position 8 on the Z axis), giving the purple point coordinates of (7,5,8). Shadows of the purple point are cast on each of the three perpendicular planes. This explains how the three coordinates (x,y,z) can specify a point anywhere in three dimensional space. All sorts of useful mathematical operations can be done using these coordinates.