ECZ 2018 · GCE Paper 2 · Question 4 — Construction and Loci

Answer the whole of this question on a sheet of plain paper.

(a(i)) Construct triangle PQR in which PQ = 10cm, QR = 8cm and angle PQR = 50°.[1]

Verified working — step 1

Draw line QR = …

(a(ii)) Measure and write the length of PR.[1]

Verified working — step 1

Using a ruler, measure the length of line PR on your constructed tri…

(b(i)) Construct the locus of points equidistant from P and Q.[1]

Verified working — step 1

With centre P and radius more than half of PQ, draw an arc above and below line PQ. Repeat with centre Q using the same radius so the arcs cross above a…

(b(ii)) Construct the locus of points equidistant from PR and PQ.[2]

Verified working — step 1

At vertex P, with centre P draw an arc cutting both PR and PQ. From each of these two points, draw arcs of equal radius that intersect each other. Join P to …

(b(iii)) Construct the locus of points 5cm from R.[1]

Verified working — step 1

With centre R and radius 5cm, draw an arc (or full ci…

(c) Label the point T which is 5cm from R and equidistant from P and Q.[1]

Verified working — step 1

Find where the perpendicular bisector of PQ (from b(i)) crosses the arc of radius 5cm centred at R (from b(iii))…

(d) Indicate by shading the region in which X must lie (≤5cm from R, nearer to Q than P, nearer to PQ than PR).[2]

Verified working — step 1

Identify the region that satisfies all three conditions: inside or on the circle of radius 5cm centred at R; on the side of the perpendicular bisector of PQ nearer …

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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