ECZ 2015 · O-Level Paper 2 · Question 8 — Geometrical Transformations
Triangle P has vertices (2, 2), (3, 1) and (3, 2). Triangle Q has vertices (-2, 2), (-3, 1) and (-3, 2).
(a) Using a scale of 2 cm to represent 1 unit on each axis, draw axes for values of x and y in the range -4 ≤ x ≤ 4 and -4 ≤ y ≤ 6. Draw and label triangles P and Q.[2]
Verified working — step 1
Scale: 2 cm to 1 unit on each axis, x from -4 to 4 and y from -4 to 6.(b) Describe fully a single transformation that maps triangle P onto triangle Q.[2]
Verified working — step 1
Compare vertices: (2, 2) → (-2, 2), (3, 1) → (-3, 1), (3, 2) → (-3, 2).(c) Triangle R is the image of triangle P after a rotation of 180° about the origin. Draw triangle R.[2]
Verified working — step 1
A rotation of 180° about the origin maps (x, y) to (-x, -y).(d) Triangle P is mapped onto triangle S with coordinates (1, -2), (2, -2) and (2, -3). Describe fully a single transformation that maps triangle P onto triangle S.[3]
Verified working — step 1
Compare vertices: (2, 2) → (1, -2), (3, 1) → (2, -3), (3, 2) → (2, -2).(e) A transformation with matrix 1002.5 maps triangle P onto triangle T. Draw and label triangle T and name this transformation.[3]
Verified working — step 1
The matrix 1002.5 sends (x, y) to (x, 2.5y).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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