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

Vectors and Translations 

Translations can be represented by vectors.

The blue rectangle is translated by the vector .

In general= 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 

• 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 

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´

To see examples of translations −