Translation

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way.

Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape.

Every point in the shape is translated the same distance in the same direction.

Triangle (PQR) moved down 3 squares and right 4 squares

Describing translations

Column vectors are used to describe translations.

\(\begin{pmatrix} 4 \\ -3 \end{pmatrix}\) means translate the shape 4 squares to the right and 3 squares down.

\(\begin{pmatrix} -2 \\ 1 \end{pmatrix}\) means translate the shape 2 squares to the left and 1 square up.

Vectors are given in the form \(\begin{pmatrix} x \\ y \end{pmatrix}\) where \(x\) is the movement horizontally and \(y\) is the movement vertically. A positive value of \(x\) means a movement to the right and a negative value of \(x\) means a movement to the left. A positive value of \(y\) means a movement upwards and a negative value of \(y\) means a movement downwards.

Example

Describe the transformation of the shape DEFG.

Transformation of shape (DEFG)

The shape has been translated by the vector \(\begin{pmatrix} -3 \\ -6 \end{pmatrix}\). The shape has moved three units to the left and six units down.