ECZ 2016 · GCE Paper 2 · Question 11 — Geometrical Transformations

The diagram shows triangle A, B, C, E and F.

(a) Describe fully a single transformation which maps triangle A onto triangle B.[2]

Verified working — step 1

Triangle B is the mirror image of A, so the transformation is a reflection.

(b) Triangle A is mapped onto triangle C by a rotation. Find

(b(i)) the angle and direction of this rotation,[2]

Verified working — step 1

Triangle C is A turned through a quarter turn, so the angle is 90°.

(b(ii)) the co-ordinates of the centre of rotation.[2]

Verified working — step 1

Join each vertex of A to its image on C.

(c) Triangle A is mapped onto triangle F by an enlargement. Find the centre and scale factor of the enlargement.[2]

Verified working — step 1

Join corresponding vertices of A and F and extend the lines; they meet at (2, 1).

(d) Triangle A is mapped onto triangle E by a shear. Find the invariant line and the matrix that represents this transformation.[4]

Verified working — step 1

A shear fixes an invariant line; here the points on the y-axis stay put, so the invariant line is 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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