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’.
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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.