7. Translations.

Given in Eqn101.gif a prefixed vector τ(α ; β), if we add this vector to every point P(x;y) of a polygon Π we obtain a polygon Π' in which every point P'(x+α;y+β) corresponds to Π in a bijective way.

The sides of Π' are equal and parallel to the corresponding sides of Π, so that the corresponding angles are equal and the two figures are congruent.

Such transformations of Π into Π' are said translations.

A translation is an isometry.