ECZ 2017 · GCE Paper 2 · Question 7 — Geometrical Transformations
Answer the whole of this question on a sheet of graph paper. Using a scale of 1 cm to represent 1 unit on each axis, draw x and y axes for -6 ≤ x ≤ 10 and -6 ≤ y ≤ 12.
(a) Quadrilateral ABCD has vertices A(1, 2), B(2, 1), C(3, 2) and D(2, 3). Quadrilateral A1B1C1D1 has vertices A1(3, 2), B1(6, 1), C1(9, 2) and D1(6, 3)
(a(i)) Draw and label quadrilaterals ABCD and A1B1C1D1.[2]
Verified working — step 1
Plot A(1, 2), B(2, 1), C(3, 2), D(2, 3) and join in order.(a(ii)) Describe fully a single transformation which maps quadrilateral ABCD onto quadrilateral A1B1C1D1.[3]
Verified working — step 1
Compare each pair: A(1, 2) → A1(3, 2), B(2, 1) → B1(6, 1), C(3, 2) → C1(9, 2), D(2, 3) → D1(6, 3).(b) The 1031, maps quadrilateral ABCD onto quadrilateral A2B2C2D2.
(b(i)) Find the coordinates of quadrilateral A2B2C2D2.[3]
Verified working — step 1
The matrix 1031 sends (x, y) to (x, 3x + y).(b(ii)) Draw and label quadrilateral A2B2C2D2.[1]
Verified working — step 1
Plot A2(1, 5), B2(2, 7),…(c) Quadrilateral A3B3C3D3 has vertices A3(-2, -4), B3(-4, -2), C3(-6, -4) and D3(-4, -6). Describe fully the transformation which maps quadrilateral ABCD onto quadrilateral A3B3C3D3.[3]
Verified working — step 1
Compare each pair: A(1, 2) → A3(-2, -4), B(2, 1) → B3(-4, -2), C(3, 2) → C3(-6, -4), D(2, 3) → D3(-4, -6).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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question