Enlarging and reducing shapes
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.
Linear Scale Factor
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 \(7 \div 4 \times 9\))