Transformations - OCREnlargement

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

Enlargement

Enlarging a shape changes its size.

Enlargement of triangle (XYZ)

All the sides of the triangle X'Y'Z' are twice as long as the sides of the original triangle XYZ. The triangle XYZ has been enlarged by a of 2.

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

To enlarge a shape, a centre of enlargement is required. When a shape is enlarged from a centre of enlargement, the distances from the centre to each point are multiplied by the scale factor.

The lengths in triangle A'B'C' are three times as long as triangle ABC. The distance from O to triangle A'B'C' is three times the distance from O to ABC.

Enlargement of triangle (ABC) to create triangle (A'B'C')

The triangle ABC has been enlarged by a scale factor of 3 about the centre of enlargement O.

Positive enlargements

A positive scale factor increases the size of a shape.

Example

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  1. Point O and triangle (ABC)

    Enlarge the triangle ABC by a scale factor of 2 about the centre of enlargement O

Alternatively, the distances OA, OB and OC can be shown as vectors. OA = \(\begin{pmatrix} 3 \\ 2 \end{pmatrix}\) so under a scale factor of 2 OA' = \(\begin{pmatrix} 6 \\ 4 \end{pmatrix}\).

The centre of enlargement may be outside an object, or it may be inside a shape, on an edge or at a corner.

The image may overlap the shape or one may be inside the other.

Question

Enlarge the triangle PQR by a scale factor of 3 about the centre of enlargement O.

Triangle (PQR) with point O at it's centre

Question

What scale factor has been used to enlarge the shape OXYZ to OX'Y'Z'?

Shape (OXYZ) enlarged

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Fractional and centre of enlargements
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