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

Diagram shows on a grid: triangle PQR with P(-2, 1), Q(-4, 4), R(-6, 2); triangle LMN with L(-1, -2), M(-4, -4), N(-2, -6); triangle L1M1N1 with L1(3, -2); trapezium ABCD with A(1, 1), B(4, 1) and trapezium A1B1C1D1 with A1(2, 2), B1(8, 2) (coordinate reads agreed by both external scripts).

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

Verified working — step 1

Compare corresponding 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

A(1,1)->A1(2,2) and B(4,1)->B1(8,2).

(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

Apply 100-3 to each vertex using (x',y') = (1x+0y, 0x-3y) = (x, -3y).

(d(i)) Triangle LMN is mapped onto triangle L1M1N1 by a shear. Find the matrix of shear.[2]

Verified working — step 1

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

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

Verified working — step 1

From the 1-201, the shear factor is the off-diagonal value k = …

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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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