ECZ 2023 · GCE Paper 2 · Question 10 — Geometrical Transformations
Answer the whole of this question on a sheet of graph paper. 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).
(a) Using a scale of 1 cm 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 the axes to the stated range.(b) Describe fully a single transformation that maps triangle ABC onto triangle A1B1C1.[3]
Verified working — step 1
Compare vertices: A(0, 4) → A1(4, 0), B(0, 6) → B1(6, 0), C(-4, 6) → C1(6, 4).(c) The 1002 maps triangle ABC onto triangle A2B2C2.
(c(i)) Find the coordinates of A2, B2 and C2.[3]
Verified working — step 1
1002 keeps x and doubles y:(c(ii)) Draw and label triangle A2B2C2.[1]
Verified working — step 1
Plot A2(0, 8), B2(0, 12), C2(-4…(d) Triangle A1B1C1 is mapped onto triangle A3B3C3 with vertices A3(4, 0), B3(6, 0) and C3(-2, 4).
(d(i)) Draw and label triangle A3B3C3.[1]
Verified working — step 1
Plot A3(4, 0), B3(6, 0…(d(ii)) Find the matrix representing this transformation.[2]
Verified working — step 1
Let M = abcd map A1B1C1 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.
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