Fractional scale factor

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

For example, a scale factor of {2} means that the side-lengths of the new shape are twice the side-lengths of the original. A scale factor of {3} means that the side-lengths of the new shape are three times the side-lengths of the original.

Therefore, a scale factor of \frac{1}{2} 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 \frac{1}{2} and centre of enlargement O, take the following steps:

Scale factor diagram

A right-angled triangle.

Question

What is the scale factor of enlargement in this diagram?

Scale factor of enlargement diagram

The scale factor of enlargement is \frac{1}{3}

Notice that OA is {6} units and OA' is {2} units.

BC is {3} units and B'C' is {1} unit, so each side on the image is \frac{1}{3} 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 {2} might be mistaken for a scale factor of \frac{1}{2}, or a scale factor of {3} mistaken for a scale factor of \frac{1}{3}.

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