Enlargements revision pack
When looking at enlargements you need a scale factor and a centre of enlargement.
Be clear which is the original shape (object) and which is the enlarged shape (image) – don’t
confuse the two!
Finding a scale factor and centre of enlargement
Points to consider:
 For it to be an enlargement, the shapes must be similar.
 Find the scale factor by comparing the lengths of similar sides.
 Find the centre of enlargement by drawing straight lines through similar points and seeing
where they cross.
 Try with at least three different lengths and points to check for errors.
Example 1
Shape P has been enlarged to give shape Q. Find the scale factor and centre of enlargement.
You should notice:
Q
The base and height of shape Q are twice that of shape
P.
The lines through three sets of similar points cross at
(0, 2)
P
Answer:
P has been enlarged by scale factor 2, centre of
enlargement (0, 2)
Example 2
Shape A has been enlarged to give shape B. Find the scale factor and centre of enlargement.
You should notice:
B
A
The base and height of shape B are three times that of
shape A
The lines through three sets of similar points cross at
(4, 6). This is an example where the centre of
enlargement lies inside the shapes.
Answer:
A has been enlarged by scale factor 3, centre of
enlargement (4, 6)
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Enlargements revision pack
Practice: Finding a scale factor and centre of enlargement
In each diagram, shape P has been enlarged to give shape Q. Find the scale factor and centre of
enlargement for each.
a)
b)
scale factor:
scale factor:
centre of enlargement:
centre of enlargement:
Q
P
Q
P
c)
scale factor:
d)
centre of enlargement:
scale factor:
centre of enlargement:
Q
P
e)
Q
P
scale factor:
f)
scale factor:
centre of enlargement:
centre of enlargement:
P
P
Q
Q
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Enlargements revision pack
When looking at enlargements you need a scale factor and a centre of enlargement.
Be clear which is the original shape (object) and which is the enlarged shape (image) – don’t
confuse the two!
Enlarging a shape by a given scale factor and centre of enlargement
Points to consider:
 Diagrams must always be drawn with a sharp pencil, and straight lines must be drawn with
a ruler.
 Leave your construction lines visible as part of your answer.
 Some questions will tell you how to label your image:
o ‘Enlarge shape P and label the image Q.’
If you are not told how to label your image, use the same letter(s) as the object followed by
an apostrophe:
o the image of A is labelled A’
o the image of triangle ABC is labelled A’B’C’
Example
Enlarge shape A by scale factor 2, centre of enlargement (0, 0).
You should:
1. Plot the centre of enlargement.
2. Draw a line from the centre of enlargement
to one corner of the shape. Extend this
line beyond the shape until it is twice as
long (as we are using scale factor 2).
3. Repeat for two other corners on the
shape.
4. Join up the corners to create the image
and label it as A’.
A
5. Check your work by comparing the lengths
of the sides. Is the height of the new
shape twice the height of the original? Are the angles unchanged?
Answer
A’
A
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Enlargements revision pack
Practice: Enlarging a shape by a given scale factor and centre of enlargement
a) Use centre of enlargement P (0, 0) and
scale factor 2 to enlarge square ABCD.
A
B
D
C
c) Use centre of enlargement P (0, 2) to
enlarge the letter M by a scale factor of 3.
Label the image as P.
b) Enlarge shape T using centre of
enlargement P (0, 5) and scale factor 2.
T
d) Use centre of enlargement P (2, 0) and
scale factor 3 to enlarge arrow Q, to give
image R.
Q
e) Use centre of enlargement P (0, 4) and
scale factor 3 to enlarge triangle ABC.
f) Use centre of enlargement P (2, 2) to
enlarge hexagon T by a scale factor ½.
T
A
C
B
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Enlargements revision pack
Answers
Finding a scale factor and centre of enlargement
a)
c)
e)
scale factor: 3
centre of enlargement: (0, 1)
scale factor: 3
centre of enlargement: (0, 5)
scale factor: 2
centre of enlargement: (0, 10)
b)
d)
f)
scale factor: 2
centre of enlargement: (1, 0)
scale factor: 2
centre of enlargement: (4, 2)
scale factor: ½
centre of enlargement: (0, 0)
Enlarging a shape by a given scale factor and centre of enlargement
b)
a)
A’
B’
T
B
D’
A
D
T’
C’
C
c)
d)
R
P
Q
e)
f)
T
A’
T’
A
C
B
C’
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Enlargements revision pack
Teaching notes
This resource addresses two enlargement techniques:
 finding a scale factor and centre of enlargement
 enlarging a shape by a given scale factor and centre of enlargement.
It contains two sets of student facing notes and example questions with accompanying practice
sheets, and is ideal for:
 a revision guide for independent revision. Students may wish to highlight and annotate the
notes and examples.
 cover lessons. You could choose whether to provide the notes for the students or as a
guide for the cover teacher.
 separate resource sheets. The practice questions are given on separate sheets so could
be used without the notes.
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