ECZ 2020 · O-Level Paper 2 · Question 11 — Geometrical Transformations

Study the diagram below to answer the questions that follow.

(a) Triangle ABC is mapped onto triangle A1B1C1 by an enlargement. Find its centre and scale factor.[2]

Verified working — step 1

Image lengths are twice the object lengths, so the scale factor is 2.

(b) Triangle ABC is mapped onto triangle A2B2C2 by a single transformation. Find

(b(i)) the matrix representing this transformation,[2]

Verified working — step 1

Compare A(1, 4) → A2(1, -8), B(3, 4) → B2(3, -8), C(3, 2) → C2(3, -4).

(b(ii)) the area scale factor of the transformation.[2]

Verified working — step 1

The area scale factor is the modulus of the determinant.

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

Verified working — step 1

Compare A(1, 4) → A3(7, 2), B(3, 4) → B3(7, 0), C(3, 2) → C3(5, 0).

(d) The 1301 maps triangle ABC onto triangle A4B4C4 (not on the diagram). Find the coordinates of A4, B4 and C4.[3]

Verified working — step 1

1301 maps (x, y) to (x + 3y, 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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