ECZ 2018 · O-Level Paper 2 · Question 10 — Geometrical Transformations

Study the diagram, which shows triangle P with vertices (2, 1), (2, 4) and (4, 1) together with triangles R, M and V, and answer the questions that follow.

(a) Triangle R is the image of triangle P under a rotation. Find the coordinates of the centre, angle and direction of the rotation.[3]

Verified working — step 1

From the diagram P has vertices (2, 1), (2, 4) and (4, 1), and R has vertices (1, -2), (4, -2) and (1, -4).

(b) A single transformation maps triangle P onto triangle M. Describe fully this transformation.[3]

Verified working — step 1

From the diagram M has vertices (4, 2), (4, 8) and (8, 2).

(c) Triangle P maps onto triangle V by a stretch. Find the matrix of this transformation.[3]

Verified working — step 1

From the diagram V has vertices (-4, 1), (-4, 4) and (-8, 1).

(d) If triangle P is mapped onto triangle S by a shear represented by the 10-21, find the coordinates of the triangle S.[3]

Verified working — step 1

The 10-21 maps (x, y) -> (x, -2x + y).

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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