ECZ 2017 · O-Level Paper 2 · Question 12 — Geometrical Transformations
Using a scale of 1 cm to represent 1 unit on each axis, draw x and y axes for -6 <= x <= 10 and -10 <= y <= 8.
(a(i)) A quadrilateral ABCD has vertices A(-5, 7), B(-4, 8), C(-3, 7) and D(-4, 4) while its image has vertices A1(-5, -3), B1(-6, -2), C1(-5, -1) and D1(-2, -2). Draw and label the quadrilateral ABCD and its image A1B1C1D1.[2]
Verified working — step 1
Plot each set of four vertices and join t…(a(ii)) Describe fully the transformation which maps quadrilateral ABCD onto quadrilateral A1B1C1D1.[3]
Verified working — step 1
The mapping is (x, y) -> (2 - y, x + 2), which is a quarter turn.(b(i)) The -2001 maps the quadrilateral ABCD onto the quadrilateral A2B2C2D2. Find the coordinates of the vertices of the quadrilateral A2B2C2D2.[2]
Verified working — step 1
The -2001 …(b(ii)) Draw and label the quadrilateral A2B2C2D2.[1]
Verified working — step 1
Plot the four image points and jo…(c) The quadrilateral ABCD is mapped onto the quadrilateral A3B3C3D3 where A3 is (4, -8), B3 is (2, -10), C3 is (0, -8) and D3 is (2, -2). Describe fully this transformation.[4]
Verified working — step 1
The mapping is (x, y) -> (-2x - 6, -2y + 6), whose linear part is -2 times the identity, so it is an enlargement of scale factor -2.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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