ECZ 2020 · GCE Paper 2 · Question 7 — Geometrical Transformations

Study the diagram below and answer the questions that follow.

(a) Triangle PQR is mapped onto triangle LMN by a single transformation. Describe this transformation fully.[3]

Verified working — step 1

Compare vertices: P(-2, 1) → L(-1, -2), Q(-4, 4) → M(-4, -4), R(-6, 2) → N(-2, -6).

(b) An enlargement maps trapezium ABCD onto trapezium A1B1C1D1. Find the centre of enlargement and the scale factor.[3]

Verified working — step 1

For an enlargement, image = k x object when centred at the origin.

(c) A transformation with the 100-3 maps triangle PQR onto triangle XYZ, not drawn on the diagram. Find the coordinates of X, Y and Z.[3]

Verified working — step 1

100-3 maps (x, y) to (x, -3y).

(d) Triangle LMN is mapped onto triangle L1M1N1 by a shear. Find

(d(i)) the matrix of shear,[2]

Verified working — step 1

A shear parallel to the x-axis has 1k01, mapping (x, y) to (x + ky, y).

(d(ii)) the shear factor.[1]

Verified working — step 1

For 1k01…

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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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