ECZ 2026 · GCE Paper 2 · Question 11 — Geometrical Transformations

Study the diagram below 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

Compare object and image: A(-3, 1) → A1(1, 3), B(-2, 4) → B1(4, 2), C(-4, 3) → C1(3, 4).

(b) An enlargement maps triangle ABC onto triangle A2B2C2. Find the centre of the enlargement and scale factor.[3]

Verified working — step 1

A(-3, 1) → A2(6, -2), B(-2, 4) → B2(4, -8), C(-4, 3) → C2(8, -6).

(c) Triangle ABC is mapped onto triangle A3B3C3 by a shear. Find the

(c(i)) matrix of this transformation,[2]

Verified working — step 1

A(-3, 1) → A3(-1, 1), B(-2, 4) → B3(6, 4), C(-4, 3) → C3(2, 3): the y-values never change.

(c(ii)) shear factor.[1]

Verified working — step 1

Shear factor = distance moved parallel to the invariant linedistance from that line.

(d) A transformation with the matrix 3001 maps triangle ABC onto triangle A4B4C4, not on the diagram. Find the coordinates of A4, B4, and C4.[3]

Verified working — step 1

3001 sends (x, y) to (3x, y) — a one-way stretch parallel to the x-axis.

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.