ECZ 2022 · O-Level Paper 2 · Question 12 — Geometrical Transformations
Study the diagram, which shows triangle ABC with vertices A(-2, 4), B(-3, 1) and C(-4, 2) together with triangles A1B1C1, A2B2C2 and A3B3C3, and answer the questions that follow.
(a) Triangle ABC is mapped onto triangle A1B1C1 by a single transformation. Describe fully this transformation.[3]
Verified working — step 1
From the diagram A(-2, 4), B(-3, 1), C(-4, 2) map to A1(4, 2), B1(1, 3), C1(2, 4).(b(i)) An enlargement maps triangle ABC onto triangle A2B2C2. Find the centre of enlargement.[1]
Verified working — step 1
From the diagram A2(4, -8)…(b(ii)) Find the scale factor.[2]
Verified working — step 1
A(-2, 4) -> A2(4, -8), B(-3, 1) -> …(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation. Find the matrix representing this transformation.[3]
Verified working — step 1
From the diagram A(-2, 4) -> A3(-2, 0), B(-3, 1) -> B3(-3, -5) and C(-4, 2) -> C3(-4, -6).(d) The transformation with 100-2 maps triangle ABC onto triangle A4B4C4, not shown on the diagram. Find the coordinates of A4, B4 and C4.[3]
Verified working — step 1
The 100-2 maps (x, y) -> (x, -2y).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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question