ECZ 2016 · O-Level Paper 2 · Question 8 — Geometrical Transformations

Study the diagram below to 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

From the centre (1, 2), A(1, 4) is 2 units above; its image A1(1, -2) is 4 units below.

(b) Triangle ABC is mapped onto triangle A2B2C2 by a shear. Find the matrix which represents this transformation.[3]

Verified working — step 1

From the diagram A(1, 4) → A2(1, 1), B(3, 4) → B2(3, -5), C(1, 5) → C2(1, 2).

(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation. Describe this transformation fully.[3]

Verified working — step 1

From the diagram A(1, 4) → A3(-4, 1), B(3, 4) → B3(-4, 3), C(1, 5) → C3(-5, 1).

(d) A transformation with matrix -3001 maps triangle ABC onto triangle A4B4C4 not drawn on the diagram. Find

(d(i)) the scale factor of this transformation,[1]

Verified working — step 1

The matrix -3001 multiplies every x by -3 and leaves y unchanged.

(d(ii)) the coordinates of A4, B4 and C4.[3]

Verified working — step 1

The matrix sends (x, y) to (-3x, 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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