INTERACTIVE 3D GEOMETRY

3D Coordinate System

In three-dimensional space, we extend the familiar 2D Cartesian plane by adding a z-axis perpendicular to both x and y axes. This creates a spatial reference system where any point can be located using three coordinates (x, y, z).

The three coordinate planes (xy, yz, zx) divide space into eight octants, similar to how axes divide a plane into four quadrants.

Distance Between Points

The distance between two points in 3D space extends the 2D distance formula by accounting for the z-coordinate:

This formula is derived from applying the Pythagorean theorem twice - first in the xy-plane, then extending into the z-dimension.

Try calculating distances between points in the interactive demo above!