Parallel translation

A parallel translation is a transformation of the plane that moves every point by the same vector. If a point $A$ is translated by vector $\vec{v}$, its image $A'$ satisfies $\overrightarrow{AA'} = \vec{v}$. Translations preserve distances and angles.

Important properties

• Translations move all points the same distance in the same direction.

• Translations preserve lengths and angles (they are isometries).

• The image of a line under a translation is a parallel line.

• Translations can be described using vectors.