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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Enlargement with a positive scale factor

Enlarging from a centre.

11 original questions, 28 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Triangle ABC has vertices at A(1, 1), B(3, 1) and C(3, 2).

Triangle ABC is enlarged by scale factor 2 with centre (0, 0).

Write down the coordinates of the vertices of the image A′, B′ and C′.

2 marks
Show answer
A′) (2, 2) B′) (6, 2) C′) (6, 4)
2

Triangle PQR has vertices at P(1, 2), Q(2, 2) and R(2, 4).

PQR is enlarged by scale factor 3 with centre (0, 0).

Write down the coordinates of P′, Q′ and R′.

2 marks
Show answer
P′) (3, 6) Q′) (6, 6) R′) (6, 12)
3

A triangle has vertices at (1, 2), (2, 2) and (1, 4).

The triangle is enlarged by scale factor 3, centre the origin.

Write down the coordinates of the vertices of the image.

2 marks
Show answer
(3, 6), (6, 6), (3, 12)
4

Triangle DEF has vertices at D(2, 4), E(6, 4) and F(6, 8).

DEF is enlarged by scale factor 12 with centre (0, 0).

Write down the coordinates of D′, E′ and F′.

2 marks
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D′) (1, 2) E′) (3, 2) F′) (3, 4)
5

Triangle ABC is enlarged to give triangle PQR.

AB = 6 cm and PQ = 15 cm. BC = 4 cm.

  1. Work out the scale factor of the enlargement.
  2. Work out the length of QR.
3 marks
Show answer
a) 2.5 b) 10
6

A triangle has vertices at (4, 2), (8, 2) and (4, 6).

The triangle is enlarged by scale factor 12, centre the origin.

Write down the coordinates of the vertices of the image.

2 marks
Show answer
(2, 1), (4, 1), (2, 3)
7

Rectangle ABCD has vertices at A(2, 1), B(6, 1), C(6, 3) and D(2, 3).

ABCD is enlarged by scale factor 1.5 with centre A.

Write down the coordinates of the vertices of the image.

3 marks
Show answer
A′) (2, 1) B′) (8, 1) C′) (8, 4) D′) (2, 4)
8

Triangle PQR has vertices at P(2, 1), Q(4, 1) and R(4, 3).

PQR is enlarged by scale factor 2 with centre (1, 1).

Write down the coordinates of P′, Q′ and R′.

3 marks
Show answer
P′) (3, 1) Q′) (7, 1) R′) (7, 5)
9

Rectangle A has vertices at (1, 1), (3, 1), (3, 2) and (1, 2).

Rectangle B has vertices at (2, 2), (6, 2), (6, 4) and (2, 4).

Describe fully the single transformation that maps rectangle A onto rectangle B.

2 marks
Show answer
Enlargement, scale factor 2, centre (0, 0).
10

Triangle S has vertices at (2, 2), (3, 2) and (2, 4).

Triangle T has vertices at (3, 3), (5, 3) and (3, 7).

Describe fully the single transformation that maps triangle S onto triangle T.

3 marks
Show answer
Enlargement, scale factor 2, centre (1, 1)
11

Triangle A has vertices at (2, 2), (4, 2) and (2, 6).

Triangle B has vertices at (1, 1), (2, 1) and (1, 3).

Triangle C has vertices at (−1, 1), (−2, 1) and (−1, 3).

  1. Describe fully the single transformation that maps triangle A onto triangle B.
  2. Describe fully the single transformation that maps triangle B onto triangle C.
4 marks
Show answer
a) enlargement, scale factor 1/2, centre (0, 0) b) reflection in the y-axis

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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