ECZ 2020 · GCE Paper 2 · Question 5 — Construction and Loci

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

(a(i)) Construct a quadrilateral PQRS in which QR = 6 cm, angle PQR = 90°, angle QRS = 120°, RS = 7 cm and PQ = 10 cm.[1]

Verified working — step 1

Draw QR = 6 cm.

(a(ii)) Measure and write the size of angle QPS.[1]

Verified working — step 1

Protractor centred at P, m…

(b) On your diagram, draw the locus of points within quadrilateral PQRS which are

(b(i)) 8 cm from R,[1]

Verified working — step 1

The locus 8 cm from the point R is a…

(b(ii)) equidistant from R and S,[1]

Verified working — step 1

Points equidistant from R and S lie …

(b(iii)) equidistant from PS and RS.[2]

Verified working — step 1

PS and RS meet at S, so points equidistant …

(c) A point X, within quadrilateral PQRS, is such that it is less than or equal to 8 cm 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

At most 8 cm from R: inside the arc from (b)(i).

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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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