ECZ 2017 · O-Level Paper 2 · Question 3 — Construction and Loci
Question from ECZ 2017 · O-Level Paper 2 · Question 3
(a) Construct a quadrilateral ABCD in which AB = 10 cm, angle ABC = 120 degrees, angle BAD = 60 degrees, BC = 7 cm and AD = 11 cm.[1]
Verified working — step 1
Draw AB = 10 cm. At A construct 60 degrees and mark AD = 11 cm. At B construct 120 degrees and mark BC = …(b) Measure and write the length of CD.[1]
Verified working — step 1
Taking A(0, 0) and B(10, 0): D = 11(cos 60, sin 60) = (5.5, 9.53) and C = B + 7(cos 60, sin 60) = …(c(i)) Within the quadrilateral ABCD, draw the locus of points which are 8 cm from A.[1]
Verified working — step 1
Set compasses to 8 cm with centre A and draw t…(c(ii)) Within the quadrilateral ABCD, draw the locus of points which are equidistant from BC and CD.[2]
Verified working — step 1
Points equidistant from two intersecting lines lie on the…(d) A point P, within the quadrilateral ABCD, is such that it is 8 cm from A and equidistant from BC and CD. Label point P.[1]
Verified working — step 1
P must satisfy both loci at once, so it is their…(e) Another point Q, within the quadrilateral ABCD, is such that it is nearer to CD than BC and greater than or equal to 8 cm from A. Indicate, by shading, the region in which Q must lie.[2]
Verified working — step 1
Nearer to CD than BC: the side of the angle-C bisector towards CD.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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