ECZ 2021 · GCE Paper 2 · Question 3 — Construction and Loci
Construction on plain paper: triangle EFG.
(a) Construct triangle EFG in which EF = 11cm, EG = 6.5cm and GF = 10cm.[1]
Verified working — step 1
Draw line EF = 11cm using a ruler.(b) Measure and write the size of angle EGF.[1]
Verified working — step 1
Using a protractor, place the centre at G…(c(i)) Within triangle EFG, construct the locus of points equidistant from EG and EF.[2]
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This locus is the angle bisector of angle E (between EG and EF).(c(ii)) Within triangle EFG, construct the locus of points 2.5cm from EF.[1]
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This locus is a line parallel to EF at a perpendicular distance of 2.5cm.(c(iii)) Within triangle EFG, construct the locus of points equidistant from E and F.[1]
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This locus is the perpendicular bisector of EF.(d) A point P, within triangle EFG, is such that it is nearer to EF than to EG, nearer to E than to F and is greater than or equal to 2.5cm away from EF. Indicate clearly by shading, the region in which P must lie.[2]
Verified working — step 1
On the triangle already drawn with the three loci from (c):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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