Describing an Enlargement
(KS3, Year 7)
The Centre of Enlargement
The centre of enlargement is the point about which a shape is enlarged.The centre of enlargement can be described using Cartesian coordinates.The Scale Factor
The scale factor describes how much larger (or smaller) the enlarged shape is compared to the original shape.The scale factor is found by dividing a length of a side of the enlarged shape to the length of the corresponding side of the original shape.How to Describe an Enlargement
Describing an enlargement is easy.Question
Describe the enlargement of the light blue shape to the dark blue shape below.Step-by-Step:
1
Find a point on the shape and the corresponding point on the enlarged shape.We will choose point A on the shape. Point A' is the corresponding point on the enlarged shape.
2
Join the pair of corresponding points with a line.
3
Find another point on the shape and the corresponding point on the enlarged shape.We will choose point B on the shape. Point B' is the corresponding point on the enlarged shape.
4
Join the pair of corresponding points with a line.
5
Draw the centre of enlargement where the two lines meet.
6
Describe the centre of enlargement in Cartesian coordinates.
In our example, the Cartesian coordinates of the centre of enlargement is (1, 0).
7
Find the length of a side on the enlarged shape.
The length of the side A'B' is 4.
8
Find the length of the corresponding side on the original shape.
The length of the side AB is 2.
9
Divide the length on the enlarged shape (4) by the length on the original shape (2).
The scale factor is 2.
$$Scale factor = \frac{A'B'}{AB}$$
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = \frac{4}{2}$$
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: = 2$$
Answer:
The shape has been enlarged about the centre of enlargement (1, 0) by a scale factor of 2.What Is an Enlargement?
An enlargement resizes a shape. An enlargement makes a shape larger or smaller. An enlargement is a type of transformation.Worksheet
This test is printable and sendable