ECZ 2018 · O-Level Paper 2 · Question 10 — Geometrical Transformations

Study the diagram below and answer the questions that follow.

(a) Triangle R is the image of triangle P under a rotation. Find the coordinates of the centre, angle and direction of the rotation.[3]

Verified working — step 1

P has vertices (2, 1), (2, 4), (4, 1); R has (1, -2), (4, -2), (1, -4).

(b) A single transformation maps triangle P onto triangle M. Describe fully this transformation.[3]

Verified working — step 1

M has vertices (4, 2), (4, 8), (8, 2).

(c) Triangle P maps onto triangle V by a stretch. Find the matrix of this transformation.[3]

Verified working — step 1

V has vertices (-4, 1), (-4, 4), (-8, 1).

(d) If triangle P is mapped onto triangle S by a shear represented by the 10-21, find the coordinates of the triangle S.[3]

Verified working — step 1

The matrix 10-21 sends (x, y) to (x, -2x + y).

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.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.