ECZ 2024 · GCE Paper 2 · Question 8 — Geometrical Transformations

Study the diagram below and answer the questions that follow.

(a) Describe fully the single transformation which maps triangle ABC onto triangle GHI.[3]

Verified working — step 1

Compare vertices: A(2, -2) → G(-2, -2), B(4, -2) → H(-2, -4), C(4, -4) → I(-4, -4).

(b) Triangle ABC is mapped onto triangle PQR by an enlargement. Find the matrix representing this transformation.[3]

Verified working — step 1

An enlargement's matrix is diagonal: k00k.

(c) A stretch represented by the 1002 maps triangle ABC onto triangle DEF (not in the diagram). Find the coordinates of D, E and F.[3]

Verified working — step 1

1002 keeps x and doubles y:

(d) Triangle KLM is the image of triangle ABC under a shear. Find the shear factor and invariant line.[3]

Verified working — step 1

The x-coordinates are unchanged, so the shear is parallel to the y-axis with invariant line x = 0.

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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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