ECZ 2023 · GCE Paper 2 · Question 10 — Geometrical Transformations
The vertices of triangle ABC are A(0, 4), B(0, 6) and C(-4, 6) while the vertices of triangle A1B1C1 are A1(4, 0), B1(6, 0) and C1(6, 4). (All coordinates printed in the question text.)
(a) Using a scale of 1cm to represent 1 unit on each axis, draw x and y axes for -4 ≤ x ≤ 8 and -3 ≤ y ≤ 12. Draw and label triangle ABC and triangle A1B1C1.[2]
Verified working — step 1
Plot axes with x from -4 to 8 and y from -3 to 12, 1 cm = …(b) Describe fully a single transformation that maps triangle ABC onto triangle A1B1C1.[3]
Verified working — step 1
Compare corresponding vertices: A(0,4)->A1(4,0), B(0,6)->B1(6,0), C(-4,6)->C1(6,4). The rule (x,y) -> (y,-x) sends A(0,4)->(4,0)=A1, B(0,6)->(6,0)=B1, C(-4,6)->(6,4) = …(c(i)) The 1002 maps triangle ABC onto triangle A2B2C2. Find the coordinates of A2, B2 and C2.[3]
Verified working — step 1
Apply the 1002 to each vertex as a column vector:(c(ii)) Draw and label triangle A2B2C2.[1]
Verified working — step 1
On the same axes, plot A2(0,8), B2(0,12), C2(-4,12) and join them to form triangle A2B2C…(d(i)) Triangle A1B1C1 is mapped onto triangle A3B3C3 with vertices A3(4, 0), B3(6, 0) and C3(-2, 4). Draw and label triangle A3B3C3.[1]
Verified working — step 1
On the same axes, plot A3(4,0), B3(6,0), C3(-2,4) and join…(d(ii)) Find the matrix representing this transformation.[2]
Verified working — step 1
Let the required matrix be M = abcd such that M*xy = x'y' for each vertex of A1B1C1 mapped to A3B3C3.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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