ECZ 2022 · GCE Paper 2 · Question 11 — Geometrical Transformations
Answer the whole of this question on a sheet of graph paper. The vertices of triangle ABC are A(-3, -3), B(-1, -3) and C(-3, -1).
(a) Using a scale of 1 cm to represent 1 unit on both axes, draw x and y axes for -6 ≤ x ≤ 8 and -4 ≤ y ≤ 8. Draw and label triangle ABC.[1]
Verified working — step 1
Draw the axes to …(b) An enlargement with centre (0, 0) and scale factor -2 maps triangle ABC onto triangle A1B1C1. Draw and label triangle A1B1C1.[2]
Verified working — step 1
Enlargement centre (0, 0), factor -2: multiply each coordinate by -2.(c) Triangle ABC is mapped onto triangle A2B2C2 with vertices A2(3, -3), B2(3, -1) and C2(1, -3).
(c(i)) Draw and label triangle A2B2C2.[1]
Verified working — step 1
Plot the given points A2(3, -3)…(c(ii)) Describe fully this single transformation.[3]
Verified working — step 1
Compare A(-3, -3) → A2(3, -3), B(-1, -3) → B2(3, -1), C(-3, -1) → C2(1, -3).(d) The 10-21 maps triangle ABC onto triangle A3B3C3. Find the coordinates of A3, B3 and C3.[3]
Verified working — step 1
10-21 sends (x, y) to (x, -2x + y).(e) A stretch with x-axis as the invariant line and scale factor -1 maps triangle ABC onto triangle A4B4C4 with vertices A4(-3, 3), B4(-1, 3) and C4(-3, 1). Find the matrix of this transformation.[2]
Verified working — step 1
A stretch with the x-axis invariant keeps x and scales y: (x, y) → (x, ky).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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