ECZ 2018 · O-Level Paper 2 · Question 4 — Construction and Loci
Question from ECZ 2018 · O-Level Paper 2 · Question 4
(a(i)) Construct a triangle XYZ in which XY = 9 cm, YZ = 7 cm and angle XYZ = 38 degrees.[1]
Verified working — step 1
Draw XY = 9 cm, construct an angle of 38 degrees at Y, mark YZ = …(a(ii)) Measure and write the length of XZ.[1]
Verified working — step 1
By the cosine rule XZ2 = 92 + 72 - 2(9)(7) cos 38(b(i)) On your diagram, within triangle XYZ, construct the locus of points which are 6 cm from Y.[1]
Verified working — step 1
Set compasses to 6 cm with centre Y …(b(ii)) On your diagram, within triangle XYZ, construct the locus of points which are equidistant from XZ and XY.[2]
Verified working — step 1
Points equidistant from two intersecting lines lie on the b…(c) Mark clearly with the letter P, within triangle XYZ, a point which is 6 cm from Y and equidistant from XZ and XY.[1]
Verified working — step 1
P satisfies both loci, so it lies w…(d) A point T, within triangle XYZ, is such that its distance from Y is less than or equal to 6 cm and it is nearer to XZ than XY. Indicate clearly, by shading, the region in which T must lie.[2]
Verified working — step 1
At most 6 cm from Y: inside the arc from (b)(i).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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