Parallel translation (other)

A parallel translation is a transformation of the plane that moves every point by the same vector. If a point $A$ has coordinates $(x, y)$, and the translation is by the vector egin{pmatrix} a \ b \\end{pmatrix}, then the image $A'$ has coordinates $(x + a, y + b)$. This transformation preserves distances and angles, so the shape and size of figures do not change.

Important properties

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

• The direction and length of the translation are determined by the translation vector.

• Translations map lines to parallel lines.

• Composing two translations results in another translation whose vector is the sum of the two vectors.