ECZ 2024 · O-Level Paper 2 · Question 10 — Geometrical Transformations

Study the following diagram and answer the questions that follow.

(a) A clockwise rotation maps triangle JKL onto triangle ABC. Find the centre and angle of this transformation.[2]

Verified working — step 1

Compare vertices: J(1, 2) → A(2, -1), K(2, 2) → B(2, -2), L(1, 4) → C(4, -1).

(b) A transformation with matrix -200-2 maps triangle JKL onto triangle XYZ, not shown on the diagram. Find the

(b(i)) scale factor of this transformation,[1]

Verified working — step 1

-200-2 is -2…

(b(ii)) coordinates of X, Y and Z.[3]

Verified working — step 1

The matrix sends (x, y) to (-2x, -2y):

(c) Triangle JKL is mapped onto triangle PQR by a stretch. Find the matrix which represents this transformation.[3]

Verified working — step 1

Compare: J(1, 2) → P(4, 2), K(2, 2) → Q(8, 2), L(1, 4) → R(4, 4).

(d) Describe fully a single transformation which maps triangle JKL onto triangle DEF.[3]

Verified working — step 1

Compare: J(1, 2) → D(-3, 2), K(2, 2) → E(-2, 2), L(1, 4) → F(-7, 4).

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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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