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Year 9 · Key Stage 3 · free KS3 maths worksheet

Transformations

14 original questions, 42 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Triangle A is drawn on the grid.

Translate triangle A by the vector 5−3. Label the image B.

−5−4−3−2−112345−5−4−3−2−112345OxyA
2 marks
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Triangle B with vertices (1, -2), (3, -2), (1, 1)
2

Triangle A has vertices at (1, 1), (3, 1) and (1, 4).

Triangle B has vertices at (5, −1), (7, −1) and (5, 2).

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

2 marks
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Translation by the vector (4, -2): 4 right and 2 down.
3

Reflect the shape in the mirror line.

2 marks
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Triangle with corners on the other side of the line, each the same distance from the line
4

Triangle T is drawn on the grid.

  1. Reflect triangle T in the line x = −1. Label the image A.
  2. Reflect triangle T in the line y = x. Label the image B.
−5−4−3−2−1123456−3−2−1123456OxyT
4 marks
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a) A at (-1, 2), (-3, 2), (-1, 5) b) B at (2, -1), (2, 1), (5, -1)
5

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

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

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

2 marks
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Reflection in the x-axis.
6

Triangle A is drawn on the grid.

  1. Rotate triangle A 180° about the origin. Label the image B.
  2. Rotate triangle A 90° anticlockwise about the point (1, −1). Label the image C.
−5−4−3−2−112345−5−4−3−2−112345OxyA(1, -1)
4 marks
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a) B at (-2, -1), (-4, -1), (-2, -4) b) C at (-1, 0), (-1, 2), (-4, 0)
7

Triangles A, B and C are drawn on the grid.

  1. Describe fully the single transformation that maps triangle A onto triangle B.
  2. Describe fully the single transformation that maps triangle A onto triangle C.
−6−5−4−3−2−1123456−4−3−2−1123456OxyABC
4 marks
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a) Rotation 90° clockwise about (0, 0) b) Rotation 180° about (-1, 1)
8

Shape A is drawn on the grid.

  1. On the grid, enlarge shape A by scale factor 2
  2. Shape A is enlarged again so that its longest side is 9 squares long. Write down the scale factor of this enlargement.
A
3 marks
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a) shape with every side twice as long, drawn anywhere on the grid b) 3
9

Triangle T and the point P (1, 1) are drawn on the grid.

Enlarge triangle T by scale factor 3, centre P.

01234567891011012345678xyTP
3 marks
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Triangle with vertices (4, 4), (10, 4), (4, 7)
10

Triangle B is an enlargement of triangle A.

  1. Write down the scale factor of the enlargement.
  2. Find the coordinates of the centre of the enlargement.
012345678012345678xyAB
3 marks
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a) 2 b) (1, 5)
11

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
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Enlargement, scale factor 2, centre (0, 0).

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

12

Triangle A and the point C (1, 1) are drawn on the grid.

Enlarge triangle A by scale factor 12, centre C.

012345678910012345678xyAC
3 marks
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Triangle with vertices (2, 2), (5, 2), (2, 4)
13

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

Triangle T is reflected in the y-axis to give triangle T1.

Triangle T1 is then reflected in the x-axis to give triangle T2.

Describe fully the single transformation that maps triangle T onto triangle T2.

3 marks
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Rotation of 180 degrees about the origin.

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

14

Triangle A is drawn on the grid.

  1. Reflect triangle A in the x-axis. Label the image B.
  2. Rotate triangle B 90° anticlockwise about the origin. Label the image C.
  3. Describe fully the single transformation that maps triangle A onto triangle C.
−5−4−3−2−112345−5−4−3−2−112345OxyA
5 marks
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a) B at (-4, -1), (-1, -1), (-4, -3) b) C at (1, -4), (1, -1), (3, -4) c) Reflection in the line y = x

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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