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


Vectors and Translations vector2.jpg

Translations can be represented by vectors.


The blue rectangle is translated by the vector Y8_Translation_02.gif.


In general=Y8_Translation_03.gif where x is the horizontal (across) movement and y is the vertical (up and down) movement.

Properties of Translation

Triangle PQR maps to triangle P´Q´R´ under the translation Y8_Translation_04.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´
Y8_Translation_06.gifPQR = Y8_Translation_06.gifP´Q´R´

area Y8_Translation_07.gifPQR = area Y8_Translation_07.gif P´Q´R´

There are no invariant points, except for the translation Y8_Translation_08.gif

Translation is a direct transformation.

i.e. Y8_Translation_07.gifPQR and Y8_Translation_07.gifP´Q´R´ are both anti-clockwise.

Translation is an isometry.

i.e. Y8_Translation_07.gif PQR is congruent to Y8_Translation_07.gifP´Q´R´

To see examples of translations − Y8_Translation_09.gif