ECZ 2015 · GCE Paper 2 · Question 9 — Geometrical Transformations

Study the diagram below and answer the questions that follow.

(i) Write the column vector representing the translation which maps Triangle P onto Triangle X,[1]

Verified working — step 1

Take a pair of corresponding vertices: (8, 5) on P maps to (2, 2) on X.

(ii) Triangle Q can be mapped onto X by a rotation. Find the coordinates of its centre and the angle of rotation.[3]

Verified working — step 1

For a 180° rotation the centre is the midpoint of each pair of corresponding vertices.

(iii) Triangle R can be mapped onto Triangle X by an enlargement. Write the coordinates of the centre and the scale factor.[3]

Verified working — step 1

Corresponding vertices: R(0, 6) to X(2, 2), R(2, 10) to X(3, 4), R(6, 6) to X(5, 2).

(iv) Triangle Q is mapped onto Triangle S by a single transformation. Find the matrix of this transformation.[3]

Verified working — step 1

Corresponding vertices: (9, 2) to (9, -2) and (12, 2) to (12, -2), while (11, 0) is unchanged.

(v) Triangle X is mapped onto Triangle T by a shear. Find the invariant line and the shear factor.[2]

Verified working — step 1

Corresponding vertices: (2, 2) to (5, 2), (5, 2) to (8, 2) and (3, 4) to (9, 4).

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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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