ECZ 2023 · O-Level Paper 2 · Question 8 — Geometrical Transformations
Study the diagram below and answer the questions that follow.
(a) Describe fully a single transformation which maps triangle ABC onto triangle A1B1C1.[3]
Verified working — step 1
Compare vertices: A(1, 2) → A1(-1, -2), B(3, 2) → B1(-3, -2), C(3, 4) → C1(-3, -4).(b) Triangle ABC is mapped onto triangle A2B2C2 (not on the diagram) by an enlargement with centre (1, 0) and scale factor 2. Find the coordinates of A2, B2 and C2.[3]
Verified working — step 1
Enlargement rule: image = centre + k(object - centre), centre (1, 0), k = 2.(c) Given that triangle A1B1C1 is mapped onto triangle A3B3C3 by a stretch, find the
(c(i)) invariant line,[1]
Verified working — step 1
Compare A1(-1, -2), B1(-3, -2), C1(-3, -4) with A3(-1, 4), B3(-3, 4), C3(-3, 8).(c(ii)) scale factor.[2]
Verified working — step 1
The y-coordinates scale: -2 → 4 a…(d) Triangle ABC is mapped onto triangle A4B4C4 by a shear. Find the matrix of this transformation.[3]
Verified working — step 1
Compare A(1, 2) → A4(5, 2), B(3, 2) → B4(7, 2), C(3, 4) → C4(11, 4).The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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