A transformation that shifts a figure in a given direction (translation vector) and over a given distance (length of the vector).

A geometric transformation that maps every segment *PQ* to a segment *P’Q’* such that the segment *PP’* is parallel to the segment *QQ’* and the segment *PQ* is parallel to the segment *P’Q’*.

Translations may be used to create frieze and tessellation.

### Properties

The invariants under a translation of the plane are the following:

- the lines that map the translation
- the parallelism of the segments in the figures and of the lines in the plane;

Translations also preserve:

- the perimeter and area of plane figures;
- the measures of angles;
- the orientation of the geometric plane
- collinearity of points.