ECZ 2020 · GCE Paper 2 · Question 5 — Construction and Loci
Construction on plain paper: quadrilateral PQRS.
(a(i)) Construct a quadrilateral PQRS in which QR = 6cm, angle PQR = 90°, angle QRS = 120°, RS = 7cm and PQ = 10cm.[1]
Verified working — step 1
Draw QR = 6cm. At Q, construct angle PQR = 90° using a protractor (or compass method), and draw QP = 10cm along this arm. At R, construct angle QRS = 120° and draw RS = …(a(ii)) Measure and write the size of angle QPS.[1]
Verified working — step 1
Using a protractor, measure the angle at P…(b(i)) Draw the locus of points 8cm from R.[1]
Verified working — step 1
With centre R and radius 8cm, draw a circle (or arc within the fi…(b(ii)) Draw the locus of points equidistant from R and S.[1]
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Join R and S with a straight line. Construct the perpendicular bisector of RS using compasses (arcs from R and S of equal…(b(iii)) Draw the locus of points equidistant from PS and RS.[2]
Verified working — step 1
At vertex S, bisect angle RSP using compasses: draw an arc cutting SR and SP, then from these points draw two more arcs to…(c) A point X, within quadrilateral PQRS, is such that it is less than or equal to 8cm from R, nearer to S than R and nearer to PS than RS. Shade the region in which X must lie.[2]
Verified working — step 1
Identify the required region: inside the circle of radius 8cm centred at R (≤8cm from R), on the side of the perpendicular bisector of RS nearer to S, and on the side of the angle bisector of angle RSP near…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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