A translation is a transformation where all points move the same distance and in the same direction.

### Notation

Translations can be represented by vectors.

T: A A´ can be shown by a vector

T = where

x is the horizontal movement and y is the vertical movement.

### Properties of Translation

Triangle PQR maps to triangle P´Q´R´ under the translation

- Lines and their images are always parallel.
e.g. PQ is parallel to P´Q´

- Length, angle size and area are invariant.

length PQ = length P´Q´ |

PQR = P´Q´R´ |

area PQR = area P´Q´R´ |

There are no invariant points, except for the translation in which all points are unchanged or invariant.

Translation is a direct transformation.

i.e. PQR and P´Q´R´ are both anti-clockwise.

Translation is an isometry.

i.e. PQR is congruent to P´Q´R´

See examples of translations −

Download an interactive spreadsheet (Microsoft Excel) showing reflections, rotations,**translations** and enlargements.

(Windows users, right click and "Save target as..." to save the files on your computer.)