ECZ 2023 · O-Level Paper 2 · Question 8 — Geometrical Transformations
Study the diagram, which shows triangle ABC with vertices A(1, 2), B(3, 2) and C(3, 4) together with triangles A1B1C1, A3B3C3 and A4B4C4, and answer the questions that follow.
(a) Describe fully a single transformation which maps triangle ABC onto triangle A1B1C1.[3]
Verified working — step 1
From the diagram A(1, 2), B(3, 2), C(3, 4) map to A1(-1, -2), B1(-3, -2), 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
For an enlargement, image = centre + k(object - centre) with centre (1, 0) and k = 2.(c(i)) Given that triangle A1B1C1 is mapped onto triangle A3B3C3 by a stretch, find the invariant line.[1]
Verified working — step 1
From the diagram A1(-1, -2), B1(-3, -2), C1(-…(c(ii)) Find the scale factor.[2]
Verified working — step 1
Each y-coordinate is multipli…(d) Triangle ABC is mapped onto triangle A4B4C4 by a shear. Find the matrix of this transformation.[3]
Verified working — step 1
From the diagram A(1, 2), B(3, 2), C(3, 4) map to A4(5, 2), B4(7, 2), 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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