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 Y10_Translation_01.gif A´ can be shown by a vectorY10_Translation_02.gif

T =Y10_Translation_03.gif 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 Y10_Translation_03.gif

  • 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´
Y10_Translation_05.gifPQR = Y10_Translation_05.gifP´Q´R´

area Y10_Translation_06.gifPQR = area Y10_Translation_06.gif P´Q´R´

There are no invariant points, except for the translation Y10_Translation_07.gifin which all points are unchanged or invariant.

Translation is a direct transformation.

i.e. Y10_Translation_06.gifPQR and Y10_Translation_06.gifP´Q´R´ are both anti-clockwise.

Translation is an isometry.

i.e. Y10_Translation_06.gif PQR is congruent to Y10_Translation_06.gifP´Q´R´

See examples of translations − button_animation.gif

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.)