4024/12 Oct/Nov 2023, Question 7: Describing Transformations
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
On a centimetre grid, identify the single transformation taking triangle P to triangle Q, then construct enlarged shape B from shape A using centre (5, 5) and area 27 cm².
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
State the one transformation that carries triangle P exactly onto triangle Q, giving all its defining details.
- 1P (5, 1), (6, 1), (6, 3) → Q (1, −5), (1, −6), (3, −6): each (x, y) → (y, −x)
- 2Rotation, 90° clockwise, centre (0, 0)
AnswerRotation, 90° clockwise, centre (0, 0)
Part (b) · 3 marks
Work out the scale factor from the areas, then draw shape B enlarged about (5, 5).
- 1Area of A = 3 cm², so area scale factor = 27 ÷ 3 = 9, length scale factor = √9 = 3
- 2Each vertex: (5, 5) + 3 × (vertex − (5, 5)), e.g. (1, 4) → (5 − 12, 5 − 3) = (−7, 2)
- 3Plot (−7, 2), (−1, 2), (−1, −4), (−4, −4), (−4, −1), (−7, −1) and join them
AnswerShape drawn at (−7, 2), (−1, 2), (−1, −4), (−4, −4), (−4, −1), (−7, −1)
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