Transformations - OCRFractional and centre of enlargements

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

Fractional enlargements and finding the centre of enlargement

Fractional enlargements

When a shape is enlarged by a between 0 and 1, the image is smaller than the original shape.

Triangle (ABC) is enlarged by 1/3 to triangle A'B'C'

The triangle ABC is enlarged by a scale factor of \(\frac{1}{3}\). All the sides of triangle A'B'C' are one third as long as the sides of the original triangle ABC.

Example

Enlarge the triangle ABC by a scale factor of \(\frac{1}{2}\) about the centre of enlargement O.

Enlarge triangle (ABC) by 1/2

First, draw ray lines from O to each corner of the triangle.

Next, measure the distance from O to each corner of ABC. Divide the distance by two and plot the points A' B' and C'. Alternatively these distances can be shown as vectors. OA = \(\begin{pmatrix} 2 \\ 2 \end{pmatrix}\) so under a scale factor of \(\frac{1}{2}\), OA' = \(\begin{pmatrix} 1 \\ 1 \end{pmatrix}\).

Finally, join up the points A' B' C'.

Triangle A'B'C' produced after enlarging triangle by 1/2

Finding the centre of enlargement

To find the centre of enlargement, draw ray lines from the corners of the image through the corners of the original shape.

Example

Describe the transformation of the triangle RST.

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  1. Triangle (STR) and triangle (S'T'R)

    Draw ray lines from the corners of triangle RST through the corners of R'S'T' until they cross. This is the centre of enlargement

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