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]

Verified working — step 1

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]

Verified working — step 1

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]

Verified working — step 1

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):

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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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