4024/21 May/Jun 2024, Question 6: Describing Transformations
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks
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The question, in short
On a grid, use triangle A with vertices (4, 1), (6, 1), (4, −3) and triangle B with vertices (−3, 1), (−2, 1), (−2, 3) to carry out translations, describe a transformation, and apply combined transformations.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Shift triangle A by the column vector (1, −3) and draw the resulting triangle P.
- 1Move each vertex 1 right and 3 down
- 2(4, 1) → (5, −2), (6, 1) → (7, −2), (4, −3) → (5, −6)
AnswerTriangle with vertices (5, −2), (7, −2) and (5, −6)
Part (b) · 3 marks
State fully the one transformation that takes triangle A onto triangle B.
- 1B is smaller and upside down: scale factor −1/2
- 2Lines through (6, 1)→(−3, 1) and (4, −3)→(−2, 3) meet at (0, 1)
- 3Enlargement, scale factor −1/2, centre (0, 1)
AnswerEnlargement, scale factor −1/2, centre (0, 1)
Part (c) · 3 marks
Reflect B in y = −1, then rotate 90° clockwise about (1, 1); draw the final triangle Q.
- 1Reflect B in y = −1: (−3, 1) → (−3, −3), (−2, 1) → (−2, −3), (−2, 3) → (−2, −5)
- 2Rotate 90° clockwise about (1, 1): (−3, −3) → (−3, 5), (−2, −3) → (−3, 4), (−2, −5) → (−5, 4)
- 3Q has vertices (−5, 4), (−3, 4) and (−3, 5)
AnswerTriangle with vertices (−5, 4), (−3, 4) and (−3, 5)
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