ECZ 2021 · O-Level Paper 2 · Question 8 — Geometrical Transformations

A point C is mapped onto a point C'(-2, 3) by a single transformation whose matrix is 1-201.

(a(i)) A point C is mapped onto C'(-2, 3) by the transformation with 1-201. Find the coordinates of the point C.[2]

Verified working — step 1

Let C = (x, y). Then 1-201xy = x - 2yy = -23.

(a(ii)) Describe fully the transformation represented by the matrix above.[3]

Verified working — step 1

The 1k01 maps (x, y) -> (x + ky, y): the y-coordinate is unch…

(b(i)) Triangle PQR with vertices P(2, 2), Q(2, 0) and R(0, 1) is mapped onto triangle P'Q'R' with vertices P'(-4, 2), Q'(-4, 0) and R'(0, 1). Find the matrix which represents this transformation.[3]

Verified working — step 1

Let the matrix be abcd.

(b(ii)) Hence, describe fully the transformation.[3]

Verified working — step 1

The matrix maps (x, y) -> (-2x, y): the y-coordinate is…

(c) F is a transformation represented by the k00k. The images of A(2, 2) and B(-2, 4) under F are A'(5, 5) and B'(-5, 10) respectively. Find the value of k.[1]

Verified working — step 1

The matrix maps (x, y) -> (kx, ky).

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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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