ECZ 2016 · GCE Paper 2 · Question 11 — Geometrical Transformations
Diagram shows triangles A, B, C, E and F on a grid.
(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. The midpoints of each pair of corresponding vertices lie on the mirror line; they lie on y = …(b(i)) Triangle A → C by a rotation. Find the angle and direction of this rotation.[2]
Verified working — step 1
Triangle C is A turned through a quarter turn; trac…(b(ii)) Find the coordinates of the centre of rotation.[2]
Verified working — step 1
Join each vertex of A to its image on C and construct the p…(c) Triangle A → F by an enlargement. Find the centre and scale factor.[2]
Verified working — step 1
Join corresponding vertices of A and F and extend; they meet at the centre of enlargement (2, 1).(d) Triangle A → E by a shear. Find the invariant line and the matrix of this transformation.[4]
Verified working — step 1
A shear fixes an invariant line and moves other points parallel to it. The points on the y-axis stay fixed, so the invariant line is x = 0.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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