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 |
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
Translation is an isometry.
i.e.
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.)
