ECZ 2025 · GCE Paper 2 · Question 9 — Geometrical Transformations

Study the following diagram and answer the questions that follow.

(a) Describe fully a single transformation that maps triangle PQR onto triangle P1Q1R1.[3]

Verified working — step 1

Compare object and image vertices: P(1, 4) → P1(-4, 1), Q(2, 4) → Q1(-4, 2), R(1, 6) → R1(-6, 1).

(b) An enlargement maps triangle PQR onto triangle P2Q2R2. Find the

(b(i)) centre of enlargement,[2]

Verified working — step 1

Lines joining each object point to its image all pass through the centre of enlargement.

(b(ii)) scale factor.[1]

Verified working — step 1

Scale factor = image distance from the centre over object distance from the centre.

(c) Triangle PQR is mapped onto triangle P3Q3R3 by a single transformation. Find the matrix of this transformation.[3]

Verified working — step 1

Let the matrix be abcd; it sends (x, y) to (ax + by, cx + dy).

(d) The transformation with 1-201 maps triangle PQR onto triangle P4Q4R4, not shown on the diagram. Find the coordinates of triangle P4Q4R4.[3]

Verified working — step 1

1-201 sends (x, y) to (x - 2y, y).

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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