ECZ 2019 · GCE Paper 2 · Question 11 — Geometrical Transformations

Study the diagram below and answer the questions that follow.

(a) An enlargement maps triangle ABC onto triangle A1B1C1. Find

(a(i)) the centre of enlargement,[1]

Verified working — step 1

Join each object vertex to its image and extend the lines.

(a(ii)) the scale factor.[1]

Verified working — step 1

Compare a point with its image: A(2, 2) → A1(-4, -4).

(b) Triangle ABC is mapped onto triangle A2B2C2 by a single transformation. Describe fully this transformation.[3]

Verified working — step 1

Compare points: A(2, 2) → A2(2, -2), B(2, 0) → B2(0, -2), C(0, 1) → C2(1, 0).

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

(c(i)) the matrix which represents this transformation,[3]

Verified working — step 1

A stretch fixes an invariant line and scales distances from it.

(c(ii)) find the area scale factor.[1]

Verified working — step 1

Area scale factor = the absolute value of the matrix determinant.

(d) A transformation 1021 maps triangle ABC onto triangle A4B4C4, not drawn on the diagram. Find the coordinates of A4, B4 and C4.[3]

Verified working — step 1

The matrix 1021 sends (x, y) to (x, 2x + 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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