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.
Describing translations
Column A vector describes a movement from one point to another. A vector quantity has magnitude (size) and direction. 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. Like a set of axes, negative numbers mean left and down movements while positive numbers mean right and up movements.
Example
Describe the transformation of the shape DEFG.
The shape has been translated by the vector \(\begin{pmatrix} -3 \\ -6 \end{pmatrix}\).
