4024/12 Oct/Nov 2021, Question 10: Describing Transformations
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Using the grid with triangles A and B, identify the single transformation linking A to B, then draw the images of A under a 90° anticlockwise rotation about (0, 0) and an enlargement of scale factor 3 about (5, −5).
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
State the one transformation, with all its details, that takes triangle A onto triangle B.
- 1(2, −4) → (6, −6): x increases by 4, y decreases by 2
- 2Translation by column vector (4, −2)
AnswerTranslation by column vector (4, −2)
Part (b) · 2 marks
On the grid, draw triangle C, the image of A after a 90° anticlockwise turn about the origin (0, 0).
- 1Rotation 90° anticlockwise about (0, 0): (x, y) → (−y, x)
- 2(2, −4) → (4, 2), (3, −4) → (4, 3), (3, −2) → (2, 3)
- 3Draw triangle C with vertices (4, 2), (4, 3), (2, 3)
AnswerTriangle at (4, 2), (4, 3), (2, 3)
Part (c) · 2 marks
On the grid, draw triangle D, the image of A after enlargement by scale factor 3 from centre (5, −5).
- 1Vector from centre (5, −5) to each vertex, ×3: (2, −4): (−3, 1) → (−9, 3); (3, −4): (−2, 1) → (−6, 3); (3, −2): (−2, 3) → (−6, 9)
- 2Add to (5, −5): (−4, −2), (−1, −2), (−1, 4)
- 3Draw triangle D with vertices (−1, −2), (−1, 4), (−4, −2)
AnswerTriangle at (−1, −2), (−1, 4), (−4, −2)
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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 10.
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