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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Enlargement with a fractional scale factor

Shapes getting smaller.

12 original questions, 35 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

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)
2

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

The rectangle is enlarged by scale factor 32, centre the origin.

Write down the coordinates of the vertices of the image.

2 marks
Show answer
(3, 3), (9, 3), (9, 6), (3, 6)
3

A triangle has vertices at (6, 3), (9, 3) and (6, 9).

The triangle is enlarged by scale factor 13, centre the origin.

Write down the coordinates of the vertices of the image.

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

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).
5

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

The triangle is enlarged by scale factor 12, centre (2, 2).

Write down the coordinates of the vertices of the image.

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

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

Triangle B has vertices at (3, 3), (5, 3) and (5, 4).

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

3 marks
Show answer
Enlargement, scale factor 1/2, centre (2, 2)
7

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)
8

A triangle has vertices at (4, 1), (4, 7) and (1, 7).

The triangle is enlarged by scale factor 23, centre (1, 1).

Write down the coordinates of the vertices of the image.

4 marks
Show answer
(3, 1), (3, 5), (1, 5)
9

Triangle P has vertices at (3, 3), (9, 3) and (3, 9).

Triangle Q has vertices at (3, 3), (5, 3) and (3, 5).

Describe fully the single transformation that maps triangle P onto triangle Q.

4 marks
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Enlargement, scale factor 1/3, centre (3, 3)
10

Triangle T has sides of length 6 cm, 8 cm and 10 cm. It has a right angle between the 6 cm and 8 cm sides.

Triangle T is enlarged by scale factor 12 to give triangle U.

  1. Write down the lengths of the sides of triangle U.
  2. Work out the area of triangle U.
3 marks
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a) 3 cm, 4 cm, 5 cm b) 6 cm2
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
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a) enlargement, scale factor 1/2, centre (0, 0) b) reflection in the y-axis
12

A triangle was enlarged by scale factor 12, centre the origin. The image has vertices at (1, 3), (4, 3) and (1, 5).

  1. Write down the coordinates of the vertices of the original triangle.
  2. Work out the area of the original triangle.
4 marks
Show answer
a) (2, 6), (8, 6), (2, 10) b) 12

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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