A scale factor can be used to enlarge or reduce a shape. A missing length on a reduction/enlargement figure can be calculated by finding its linear scale factor.

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A **scale factor** can be used to enlarge or reduce a shape.

Shape A below is enlarged by scale factor \(2\) to give Shape B.

The scale factor describes the **size** of an enlargement or reduction.

For example, a scale factor of \(2\) means that the new shape is twice the size of the original.

A scale factor of \(3\) means that the new shape is three times the size of the original.

A scale factor of \(\frac{1}{2}\) means that the new shape is half the size of the original.

To calculate the scale factor, we use the following:

\[SF_{Enlargement}=\frac{Big}{Small}\]

\[SF_{Reduction}=\frac{Small}{Big}\]

You can get the 'big' and 'small' from the corresponding sides on the figures.

- Question
Rectangles \(PQRS\) is an enlargement of rectangle \(pqrs\). What is the length of \(PS\)?

\(PS\) is on the bigger rectangle, therefore we will be using an

**enlargement**scale factor.\[SF_{Enlargement}= \frac{Big}{Small}=\frac{7}{4}\]

Therefore \(PS\) is \(\frac{7}{4}\) times \(ps\).

So, \(PS = \frac{7}{4} \times 9 = 15.75cm\)

(You can type in your calculator \(7 \div 4 \times 9\))