# Fractional scale factor

You already know that the size of an enlargement is described by its scale factor.

For example, a scale factor of means that the side-lengths of the new shape are twice the side-lengths of the original. A scale factor of means that the side-lengths of the new shape are three times the side-lengths of the original.

Therefore, a scale factor of means that the side-lengths of the new shape are half the side-lengths of the original.

When the scale factor is fractional and the shape decreases in size, we still call it an enlargement.

## Example

To enlarge the triangle with a scale factor of and centre of enlargement O, take the following steps:

A right-angled triangle.

Question

What is the scale factor of enlargement in this diagram?

The scale factor of enlargement is Notice that OA is units and OA' is units.

BC is units and B'C' is unit, so each side on the image is of the length of the original shape.

Always check which shape is the object and which shape is the image, to avoid confusing the scale factors. For example, a scale factor of might be mistaken for a scale factor of , or a scale factor of mistaken for a scale factor of .

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