Transformations

4) Translation

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

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.

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

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

Vectors are given in the form of \left(\begin{array}{c}x\ y\end{array}\right) 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 \left(\begin{array}{c}-3\ -6\end{array}\right) . The shape has moved three units to the left and six units down.


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