ECZ 2021 · GCE Paper 2 · Question 11 — Geometrical Transformations

The vertices of triangle ABC are A(40, 30), B(40, 70) and C(70, 70) while those of triangle A1B1C1 are A1(20, 15), B1(20, 35) and C1(35, 35). (All coordinates printed in the question text.)

(a) Using a scale of 2cm to represent 10 units on each axis for values of x and y from 0 to 70, draw and label triangles ABC and A1B1C1.[2]

Verified working — step 1

Draw x and y axes from 0 to 70, using 2cm to represent 10 units on each axis. Plot A(40,30), B(40,70), C(70,70) and join them …

(b) Describe fully a single transformation that maps triangle ABC onto triangle A1B1C1.[3]

Verified working — step 1

Compare corresponding vertices:

(c) A rotation of 180° about (20, 40) maps triangle A1B1C1 onto triangle A2B2C2. Determine the coordinates of A2, B2 and C2.[3]

Verified working — step 1

For a rotation of 180° about a centre (a,b), the image of a point (x,y) is found using the rule:

(d(i)) Triangle A1B1C1 is mapped onto triangle A3B3C3 with vertices A3(40, 15), B3(40, 35) and C3(70, 35). Draw and label triangle A3B3C3.[1]

Verified working — step 1

Plot A3(40,15), B3(40,35), C3(70,35) on the same grid a…

(d(ii)) Describe fully this transformation.[3]

Verified working — step 1

Compare coordinates of A1B1C1 and A3B3C3:

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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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