ECZ 2024 · GCE Paper 2 · Question 2 — Construction and Loci

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

(a) Construct a quadrilateral PQRS in which PQ = 10 cm, angle SPQ = 70°, QR = 6.5 cm, PS = 5 cm and SR = 7 cm.[1]

Verified working — step 1

Draw PQ = 10 cm.

(b) Measure and write the angle PQR.[1]

Verified working — step 1

Protractor centred at Q with the ze…

(c) On your diagram, construct the locus of points within the quadrilateral PQRS which are

(c(i)) 3 cm from PQ,[1]

Verified working — step 1

The locus 3 cm from the line PQ is a paral…

(c(ii)) equidistant from PS and SR.[2]

Verified working — step 1

PS and SR meet at S, so points equidistant …

(d) L is a point inside quadrilateral PQRS such that it is 3 cm from PQ and equidistant from PS and SR. Label the point L.[1]

Verified working — step 1

L satisfies both c…

(e) M is another point inside quadrilateral PQRS such that it is less than or equal to 3 cm 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

At most 3 cm from PQ: the strip between PQ and the parallel line.

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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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