ECZ 2021 · GCE Paper 2 · Question 3 — Construction and Loci
Answer the whole of this question on a sheet of plain paper.
(a) Construct triangle EFG in which EF = 11 cm, EG = 6.5 cm and GF = 10 cm.[1]
Verified working — step 1
Draw EF = 11 cm (the longest side).(b) Measure and write the size of angle EGF.[1]
Verified working — step 1
Protractor centred at G, measuring between GE and GF.(c) Within triangle EFG, construct the locus of points which are
(c(i)) equidistant from EG and EF,[2]
Verified working — step 1
EG and EF meet at E, so points equidistant…(c(ii)) 2.5 cm from EF,[1]
Verified working — step 1
The locus 2.5 cm from the line EF is a line pa…(c(iii)) equidistant from E and F.[1]
Verified working — step 1
Points equidistant from E and F lie …(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 2.5 cm away from EF. Indicate clearly by shading, the region in which P must lie.[2]
Verified working — step 1
Nearer to EF than EG: the EF side of the bisector of angle E 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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