ECZ 2020 · O-Level Paper 2 · Question 11 — Geometrical Transformations

Study the diagram, which shows triangle ABC with vertices (1, 4), (3, 4) and (3, 2) together with triangles A1B1C1, A2B2C2 and A3B3C3, and answer the questions that follow.

(a) Triangle ABC is mapped onto triangle A1B1C1 by an enlargement. Find its centre and scale factor.[2]

Verified working — step 1

From the diagram A(1, 4), B(3, 4), C(3, 2) map to A1(-3, 2), B1(1, 2), C1(1, -2).

(b(i)) Triangle ABC is mapped onto triangle A2B2C2 by a single transformation. Find the matrix representing this transformation.[2]

Verified working — step 1

From the diagram A(1, 4) -> A2(1, -8), B(3, 4) -> B2(3, -8) and C(3, 2) -> C2(3, -4).

(b(ii)) Find the area scale factor of the transformation.[2]

Verified working — step 1

The area scale factor is the modulus of the determinant of the matrix.

(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation. Describe fully this transformation.[3]

Verified working — step 1

From the diagram A(1, 4), B(3, 4), C(3, 2) map to A3(7, 2), B3(7, 0), C3(5, 0).

(d) The 1301 maps triangle ABC onto triangle A4B4C4 (not on the diagram). Find the coordinates of A4, B4 and C4.[3]

Verified working — step 1

The 1301 maps (x, y) -> (x + 3y, 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.