ECZ 2022 · GCE Paper 2 · Question 11 — Geometrical Transformations
The vertices of triangle ABC are A(-3, -3), B(-1, -3) and C(-3, -1). (All coordinates printed in the question text.)
(a) Using a scale of 1cm 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 x-axis from -6 to 8 and y-axis from -4 to 8, using 1cm = …(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), scale factor -2: multiply each coordinate by -2.(c(i)) Triangle ABC is mapped onto triangle A2B2C2 with vertices A2(3, -3), B2(3, -1) and C2(1, -3). Draw and label triangle A2B2C2.[1]
Verified working — step 1
Plot the given points A2(3,-3), B2(3,-1) and C2(1,-3) on the same…(c(ii)) Describe fully this single transformation.[3]
Verified working — step 1
Compare corresponding vertices: 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
Apply the 10-21 to each vertex using (x') = 10-21(x,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 means every point (x,y) maps to (x, ky) for scale factor k, since x stays the same (invariant line) and y is scaled.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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