Fractional enlargements and finding the centre of enlargement
Fractional enlargements
When a shape is enlarged by a The ratio of corresponding lengths in similar shapes, ie how much larger or smaller the shapes are. between 0 and 1, the image is smaller than the original shape.
The triangle ABC is enlarged by a scale factor of \(\frac{1}{3}\). All the sides of triangle A'B'C' are \(\frac{1}{3}\) 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.
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 2 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'.
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.
Image caption, 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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