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Grade 6 · Higher · free GCSE maths worksheet

Enlargement with a negative scale factor

Inverted enlargements.

11 original questions, 26 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 point is enlarged by scale factor −2, centre (0, 0). Write down the coordinates of the image of

  1. the point P (3, 2),
  2. the point Q (−1, 4).
2 marks
Show answer
a) (-6, -4) b) (2, -8)
2

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

Triangle P is enlarged by scale factor −1, centre (0, 0), to give triangle Q.

Write down the coordinates of the vertices of triangle Q.

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

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

Triangle A is enlarged by scale factor −2, centre (0, 0), to give triangle B.

Write down the coordinates of the vertices of triangle B.

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

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

Triangle T is enlarged by scale factor −12, centre (0, 0), to give triangle U.

Write down the coordinates of the vertices of triangle U.

2 marks
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(-2, -1), (-3, -1), (-2, -3)
5

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

Triangle M is enlarged by scale factor −3, centre (1, 0), to give triangle N.

Work out the coordinates of the vertices of triangle N.

2 marks
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(-2, -3), (-5, -3), (-2, -9)
6

Triangle R is drawn on the grid with vertices at (2, 3), (4, 3) and (2, 4).

On the grid, enlarge triangle R by scale factor −2, centre (1, 2).

−6−5−4−3−2−11234567−4−3−2−1123456OxyR
2 marks
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Triangle with vertices (-1, 0), (-5, 0), (-1, -2)
7

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

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

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

−6−5−4−3−2−11234567−4−3−2−1123456OxyAB
2 marks
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Enlargement, scale factor -12, centre (0, 0)
8

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

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

B is an enlargement of A. Describe fully the enlargement.

3 marks
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Enlargement, scale factor -1/2, centre (0, 0)
9

Triangle P has vertices at (3, 1), (5, 1) and (3, 2).

Triangle Q has vertices at (0, 1), (−4, 1) and (0, −1).

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

−6−5−4−3−2−11234567−4−3−2−1123456OxyPQ
3 marks
Show answer
Enlargement, scale factor -2, centre (2, 1)
10

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

  1. Triangle A is enlarged by scale factor −12, centre (0, 0), to give triangle B. Write down the coordinates of the vertices of triangle B.
  2. Describe fully the single transformation that maps triangle B back onto triangle A.
−6−5−4−3−2−11234567−4−3−2−1123456OxyA
3 marks
Show answer
a) (-1, -1), (-3, -1), (-3, -2) b) Enlargement, scale factor -2, centre (0, 0)
11

Triangle A has vertices (3, 2), (4, 2) and (3, 3).

Triangle B has vertices (−1, −2), (−4, −2) and (−1, −5).

B is an enlargement of A. Describe fully the enlargement.

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

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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