ECZ 2013 · O-Level Paper 2 · Question 8 — Geometrical Transformations
Triangle S has vertices (1, 1), (2, 1) and (1, 2) while triangle R has vertices (2, 3), (3, 3) and (2, 4).
(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 -5 ≤ x ≤ 5 and -5 ≤ y ≤ 4. Draw and label triangles S and R.[2]
Verified working — step 1
Scale: 2 cm to 1 unit on each axis, x from -5 to 5 and y from -5 to 4.(b) Describe fully a single transformation that maps triangle S onto triangle R.[2]
Verified working — step 1
Compare vertices: (1, 1) → (2, 3), (2, 1) → (3, 3), (1, 2) → (2, 4).(c(i)) Triangle T has vertices (-2, -2), (-4, -2) and (-2, -4). Draw and label triangle T.[1]
Verified working — step 1
Plot the vertices (-2, -2…(c(ii)) Write the matrix of the transformation that maps triangle S onto triangle T.[3]
Verified working — step 1
Compare vertices: (1, 1) → (-2, -2), (2, 1) → (-4, -2), (1, 2) → (-2, -4).(d) Triangle S is mapped onto triangle W with vertices (3, 1), (4, 1) and (5, 2). Draw triangle W and describe this transformation fully.[4]
Verified working — step 1
Compare vertices: (1, 1) → (3, 1), (2, 1) → (4, 1), (1, 2) → (5, 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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