Transformations - OCRTranslation

Transformations change the size or position of shapes. Congruent shapes are identical, but may be rotated or reflected. Scale factors show how much larger or smaller similar shapes are.

Part ofMathsGeometry and measure

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 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.

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