KS3 Maths · Year 7 · Chapter 11: Shape and ratio · Lesson 2

Fractional enlargement

Year 7About 75 minutesNo calculator45 marks

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Date

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Quick questions to start.

A1
Needed today
Work out $\frac{1}{3}$ of $18$ .
[1 mark]
Answer
A2
Needed today
Work out $\frac{2}{3}$ of $15$ .
[1 mark]
Answer
A3
Last lesson
Two squares have sides of $2$ cm and $6$ cm. Write the ratio of their areas in its simplest form.
[1 mark]
Answer
A4
From chapter 2
A side of a shape is $3$ cm long. The shape is enlarged by a scale factor of $4$ . How long is this side on the image?
[1 mark]
Answer

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Triangle $T$ is enlarged by a scale factor of $\frac{1}{2}$ about the origin. Write down the coordinates of the vertices of the image.

Hint About the origin, multiply each coordinate by the scale factor.

B1
Triangle $S$ is enlarged by a scale factor of $\frac{1}{3}$ about the origin. Write down the coordinates of the vertices of the image.
[3 marks]
Answer

Example 2

Rectangle $R$ is enlarged by a scale factor of $\frac{1}{2}$ about the centre $C (1, 1)$ . Write down the coordinates of the vertices of the image.

Hint Count across and up from

C

to each vertex, halve both, and count that far from

C

B2
Triangle $Q$ is enlarged by a scale factor of $\frac{1}{3}$ about the centre $C (2, 1)$ . Write down the coordinates of the vertices of the image.
[3 marks]
Answer

Example 3

Rectangle $B$ is an enlargement of rectangle $A$ . Work out the scale factor and the coordinates of the centre of enlargement.

Hint Scale factor

=

a length on the image

\div

the same length on the object. Join each vertex to its image and extend the lines until they meet.

B3
Triangle $B$ is an enlargement of triangle $A$ . Work out the scale factor and the coordinates of the centre of enlargement.
[3 marks]
Answer

Year 7

C1
The points $A (12, 6)$ , $B (8, 10)$ and $C (4, 2)$ are enlarged by a scale factor of $\frac{1}{2}$ about the origin. Write down the coordinates of the images $A^{'}$ , $B^{'}$ and $C^{'}$ .
[2 marks]
Answer
C2
A triangle has vertices $(9, 6)$ , $(12, 0)$ and $(3, 3)$ . It is enlarged by a scale factor of $\frac{2}{3}$ about the origin. Write down the coordinates of the vertices of the image.
[2 marks]
Answer

C3
Rectangle $B$ is an enlargement of rectangle $A$ . (a) Write down the scale factor of the enlargement from $A$ to $B$ . (b) Write down the scale factor of the enlargement from $B$ to $A$ .
[2 marks]
Answer
C4
Enlarge the triangle by a scale factor of $\frac{1}{2}$ about the centre $C$ . Draw the image on the grid.
[2 marks]
C5
Rectangle $A$ is $18$ cm long and $12$ cm wide. Rectangle $B$ is an enlargement of $A$ . The length of $B$ is $6$ cm. Work out the scale factor of the enlargement from $A$ to $B$ , and the width of $B$ .
[3 marks]
Answer

GCSE Foundation

D1
Aisha says, "Triangle $T$ has angles of $36°$ , $64°$ and $80°$ . When it is enlarged by a scale factor of $\frac{1}{2}$ , its angles become $18°$ , $32°$ and $40°$ ."
Explain why Aisha is wrong, and write down the angles of the image.
[3 marks]
Answer

D2
Square $B$ is an enlargement of square $A$ .
(a)
Write down the scale factor of the enlargement from $A$ to $B$ .
[1 mark]
Answer
(b)
Find the coordinates of the centre of enlargement.
[2 marks]
Answer
(c)
Square $B$ is enlarged by a scale factor of $2$ about the same centre to give square $D$ . Write down the coordinates of the vertex of $D$ that is furthest from the centre.
[2 marks]
Answer
Total for D2: 5 marks
D3
The point $P (24, 12)$ is enlarged by a scale factor of $\frac{1}{2}$ about the origin to give $P^{'}$ . Then $P^{'}$ is enlarged by a scale factor of $\frac{1}{3}$ about the origin to give $P^{''}$ . Work out the coordinates of $P^{''}$ , and the scale factor of the single enlargement about the origin that takes $P$ straight to $P^{''}$ .
[4 marks]
Answer
D4
Triangle $A B C$ is enlarged by a scale factor of $\frac{3}{4}$ to give triangle $A^{'} B^{'} C^{'}$ . $A^{'} B^{'} = 9$ cm, $B C = 20$ cm and angle $A B C = 50°$ .
Not drawn accurately
(a)
Work out the length of $A B$ .
[2 marks]
Answer
(b)
Work out the length of $B^{'} C^{'}$ .
[1 mark]
Answer
(c)
Write down the size of angle $A^{'} B^{'} C^{'}$ .
[1 mark]
Answer
Total for D4: 4 marks

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can enlarge a shape by a fractional scale factor about the origin or another centre.
I can find the scale factor and the centre of an enlargement.
I can work out lengths and areas of the image, and I know the angles do not change.
I can combine two enlargements into one.

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