ECZ 2016 · O-Level Paper 2 · Question 8 — Geometrical Transformations
Study the diagram, which shows triangle ABC with vertices A(1, 4), B(3, 4) and C(1, 5) together with its images, to answer the questions that follow.
(a(i)) An enlargement maps triangle ABC onto triangle A1B1C1. Find the centre of enlargement.[1]
Verified working — step 1
Join A to A1, B to B1 and C to C1 and …(a(ii)) Find the scale factor.[1]
Verified working — step 1
From the centre (1, 2), A(1, 4) is 2 units above while A1(1, -2) is 4 units below.(b) Triangle ABC is mapped onto triangle A2B2C2 by a shear. Find the matrix which represents this transformation.[3]
Verified working — step 1
From the diagram A(1, 4) -> A2(1, 1), B(3, 4) -> B2(3, -5) and C(1, 5) -> C2(1, 2).(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation. Describe this transformation fully.[3]
Verified working — step 1
From the diagram A(1, 4) -> A3(-4, 1), B(3, 4) -> B3(-4, 3) and C(1, 5) -> C3(-5, 1).(d(i)) A transformation with -3001 maps triangle ABC onto triangle A4B4C4, not drawn on the diagram. Find the scale factor of this transformation.[1]
Verified working — step 1
The -3001 multiplies every x-coordinate by -3 and le…(d(ii)) Find the coordinates of A4, B4 and C4.[3]
Verified working — step 1
A(1, 4), B(3, 4) and C(1, 5…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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