ECZ 2010 · O-Level Paper 2 · Question 12 — Geometrical Transformations
Question from ECZ 2010 · O-Level Paper 2 · Question 12
(a) Using a scale of 1 cm to represent 1 unit on each axis, draw x and y axes for -5 ≤ x ≤ 8 and 2 ≤ y ≤ 12. Draw and label triangle PQR whose vertices are P(5, 2), Q(1, 1) and R(3, 6).[1]
Verified working — step 1
Scale: 1 cm to 1 unit on each axis, x from -5 to 8 and y from 2 to 12.(b) An enlargement maps triangle PQR onto triangle PAB. Given that the co-ordinates of A are (-3, 0), find
(b(i)) the centre of enlargement,[1]
Verified working — step 1
P appears in both triangle names PQR and PAB, so P does not move.(b(ii)) the scale factor,[1]
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Q(1, 1) maps to A(-3, 0).(b(iii)) the co-ordinates of the point B,[1]
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R(3, 6) is the object, and PR = (3 - 5, 6 - 2) = (-2, 4).(b(iv)) the ratio of the area of triangle PAB to triangle PQR.[1]
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Areas scale by the SQUARE of the linear scale factor.(c) Given that C is the point (2, 5), D is the point (6, 3) and that a single transformation maps triangle PQR onto triangle CQD,
(c(i)) describe fully the single transformation,[2]
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Compare vertices: P(5, 2) → C(2, 5), Q(1, 1) → itself, R(3, 6) → D(6, 3).(c(ii)) write down the matrix of this transformation.[1]
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A reflection in y = x sends (x, y) to (y, x).(d) Given that PQRS is a parallelogram,
(d(i)) write down the co-ordinates of S,[1]
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In parallelogram PQRS the diagonals bisect each other.(d(ii)) describe the transformation which maps triangle PQR onto triangle RSP.[3]
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P maps to R, Q maps to S and R maps to P.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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