GCSE Maths revision · Geometry and measures

Enlargement

Foundation and Higher

The idea

An enlargement multiplies every distance from the centre by the scale factor. A scale factor of $\tfrac{1}{2}$ makes the shape smaller and moves it towards the centre.

Draw a line from the centre to each vertex.
Multiply that distance by the scale factor to place the new vertex.
Join the new vertices; check each side has been multiplied by the scale factor.

Watch out A scale factor between $0$ and $1$ still enlarges from the centre; the image just ends up closer to it.

See it worked

Worked exampleNon-calculator3 marks

This question is about enlargements.

(a) A rectangle measures 2 cm by 5 cm. It is enlarged by scale factor 3. Work out the perimeter of the enlarged rectangle.

(b) A square with side 4 cm is enlarged to a square with side 10 cm. Write down the scale factor.

(a) Every length is multiplied by 3: 6 cm by 15 cm.
$2 \times (6 + 15) = 42$
(b) Scale factor $= \frac{\text{new length}}{\text{old length}} = \frac{10}{4} = 2.5$ .

Answer (a) 42 cm; (b) 2.5

Your turn

Question 1Non-calculator5 marks

An enlargement has centre C $(1,-2)$ and scale factor $1/2$ . Point A is $(7,1)$ .

(a) Find the coordinates of the image of A.

(b) A segment of length 9 cm is enlarged in the same way. Find its image length.

Question 2Non-calculator3 marks

Rectangle R has vertices (2, 2), (6, 2), (6, 4) and (2, 4). It is enlarged by scale factor $\frac{1}{2}$ with centre (0, 0).

(a) Write down the coordinates of the image of (6, 4).

(b) Work out the area of the image.

Question 3Non-calculator4 marks

The line segment $AB$ has $A(1, 2)$ and $B(3, 2)$ . It is enlarged to give $A'B'$ with $A'(-1, -1)$ and $B'(5, -1)$ .

(a) Write down the scale factor of the enlargement.

(b) Find the coordinates of the centre of enlargement.

In past papers

34 official questions in 34 papers since 2017. The latest:

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