ECZ 2021 · GCE Paper 2 · Question 11 — Geometrical Transformations

Answer the whole of this question on a sheet of graph paper. The vertices of triangle ABC are A(40, 30), B(40, 70) and C(70, 70) while that of triangle A1B1C1 are A1(20, 15), B1(20, 35) and C1(35, 35).

(a) Using a scale of 2 cm to represent 10 units on each axis for values of x and y from 0 to 70, draw and label triangles ABC and A1B1C1.[2]

Verified working — step 1

Draw the axes to the stated range.

(b) Describe fully a single transformation that maps triangle ABC onto triangle A1B1C1.[3]

Verified working — step 1

Compare vertices: each image coordinate is half the object's.

(c) A rotation of 180° about (20, 40) maps triangle A1B1C1 onto triangle A2B2C2. Determine the coordinates of A2, B2 and C2.[3]

Verified working — step 1

A 180-degree rotation about (a, b) sends (x, y) to (2a - x, 2b - y), with centre (20, 40): (40 - x, 80 - y).

(d) Triangle A1B1C1 is mapped onto triangle A3B3C3 by a single transformation with vertices A3(40, 15), B3(40, 35) and C3(70, 35).

(d(i)) Draw and label triangle A3B3C3.[1]

Verified working — step 1

Plot A3(40, 15), B3(40, …

(d(ii)) Describe fully this transformation.[3]

Verified working — step 1

Compare A1(20, 15) → A3(40, 15), B1(20, 35) → B3(40, 35), C1(35, 35) → C3(70, 35).

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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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