ECZ 2022 · O-Level Paper 2 · Question 12 — Geometrical Transformations

Study the following diagram and answer the questions that follow.

(a) Triangle ABC is mapped onto triangle A1B1C1 by a single transformation. Describe fully this transformation.[3]

Verified working — step 1

Compare vertices: A(-2, 4) → A1(4, 2), B(-3, 1) → B1(1, 3), C(-4, 2) → C1(2, 4).

(b) An enlargement maps triangle ABC onto triangle A2B2C2. Find the

(b(i)) centre of enlargement,[1]

Verified working — step 1

For an enlargement, the lines joining each object point to its image meet at the centre.

(b(ii)) scale factor.[2]

Verified working — step 1

Compare distances from the centre: A(-2, 4) -…

(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation. Find the matrix representing this transformation.[3]

Verified working — step 1

Compare A(-2, 4) → A3(-2, 0), B(-3, 1) → B3(-3, -5), C(-4, 2) → C3(-4, -6).

(d) The transformation with matrix 100-2 maps triangle ABC onto triangle A4B4C4 not shown on the diagram. Find the coordinates of A4, B4 and C4.[3]

Verified working — step 1

100-2 keeps x and multiplies y by -2:

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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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