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