ECZ 2016 · GCE Paper 2 · Question 4 — Construction and Loci
Answer the whole of this question on a sheet of plain paper.
(a) Construct triangle PQR in which PQ = 10 cm, PR = 8.5 cm and QR = 9 cm.[1]
Verified working — step 1
Draw PQ = 10 cm.(b) Measure and write the size of angle PRQ.[1]
Verified working — step 1
Place the protractor centre at R with the baseline along RP.(c) On your diagram, draw the locus of points which are
(c(i)) 5.5 cm from P,[1]
Verified working — step 1
The locus 5.5 cm from P …(c(ii)) equidistant from P and R,[1]
Verified working — step 1
Equidistant from the two POINTS P and R…(c(iii)) equidistant from PR and PQ.[2]
Verified working — step 1
PR and PQ meet at P, so points equidistant …(d) A point S inside triangle PQR is such that S is: less than or equal to 5.5 cm from P, nearer to P than to R, nearer to PR than to PQ. Indicate clearly, by shading, the region in which S must lie.[2]
Verified working — step 1
At most 5.5 cm from P: inside the circle from (c)(i).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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