# A sign records direction

Authored explanation; editorial review pending.

Put the starting point at zero on a ruler. A final mark three units right has displacement +3; one three units left has displacement −3. Adding the signed displacements gives zero. Adding the distances from the start gives six.

Displacement compares the final and initial positions. It is not the length of the path travelled between them.

## Worked example

Two walkers both finish one unit from their start, one at −1 and the other at +1. The signed average is zero. The average distance is one.

The sign names a direction relative to a chosen axis; it does not mean a negative distance.