ECZ 2024 · GCE Paper 2 · Question 2 — Construction and Loci
Construction on plain paper: quadrilateral PQRS.
(a) Construct a quadrilateral PQRS in which PQ = 10cm, angle SPQ = 70°, QR = 6.5cm, PS = 5cm and SR = 7cm.[1]
Verified working — step 1
1. Draw line PQ = 10cm.(b) Measure and write the angle PQR.[1]
Verified working — step 1
Using a protractor, place the centre on Q…(c(i)) On your diagram, construct the locus of points within the quadrilateral PQRS which are 3cm from PQ.[1]
Verified working — step 1
The locus of points 3cm from line PQ (within the quadrilateral) is a straight line drawn parall…(c(ii)) On your diagram, construct the locus of points within the quadrilateral PQRS which are equidistant from PS and SR.[2]
Verified working — step 1
Points equidistant from PS and SR lie on the angle bisector of angle PSR.(d) L is a point inside quadrilateral PQRS such that it is 3cm from PQ and equidistant from PS and SR. Label the point L.[1]
Verified working — step 1
L is the point where the two loci from (c)(i) and (c)(ii) intersect, i.e. where the line parallel…(e) M is another point inside quadrilateral PQRS such that it is less than or equal to 3cm from PQ and nearer to PS than to SR. Indicate clearly, by shading, the region in which M must lie.[2]
Verified working — step 1
Shade the region that satisfies both conditions: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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