Linear scale factor
The size of an enlargement/reduction is described by its scale factor.
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.
To calculate the scale factor, we use the following:
\(S{F_{enlargement}} = \frac{{Big}}{{Small}}\)
\(S{F_{{\mathop{\rm re}\nolimits} duction}} = \frac{{Small}}{{Big}}\)
You can get the 'big' and 'small' from the corresponding sides on the figures.
Example
The rectangles pqrs and PQRS are similar. What is the length of PS?
Answer
PS is on the bigger rectangle, therefore we will be calculating an enlargement scale factor first.
\(S{F_{enlargement}} = \frac{{Big}}{{Small}} = \frac{7}{4}\)
Therefore rectangle PQRS is \(\frac{7}{4}\) times bigger than rectangle pqrs.
So, \(PS = \frac{7}{4} \times 9 = 15.75cm\)
(You can type in your calculator 7 梅 4 脳 9)
Now try these example questions.
Question
wxyz and WXYZ are similar figures. What is the length of XY?
XY is on the bigger figure, therefore we will be calculating the enlargement scale factor.
\(S{F_{enlargement}} = \frac{{Big}}{{Small}} = \frac{9}{8}\)
Therefore rectangle PQRS is \(\frac{9}{8}\) times bigger than rectangle pqrs.
So, \(PS = \frac{9}{8} \times 4 = 4.5cm\)
Question
What is the size of angle WXY?
Remember that the angles in similar figures stay the same, so angle WXY is 57掳.
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates