ECZ 2025 · GCE Paper 2 · Question 5 — Construction and Loci
Construction on plain paper: triangle ABC.
(a(i)) Construct triangle ABC in which AB = 10 cm, AC = 8 cm and angle BAC = 100°.[1]
Verified working — step 1
Draw line AB = 10 cm using a ruler. At A, use a protractor to measure an angle of 100° from AB and draw a ray from A. On this ray, mark point C such that AC = …(a(ii)) Measure and write the length of BC.[1]
Verified working — step 1
Using a ruler, measure the length of line BC dire…(b(i)) On your diagram, draw the locus of points within triangle ABC which are 7 cm from C.[1]
Verified working — step 1
Open a compass to a radius of 7 cm. With centre C, draw an arc w…(b(ii)) On your diagram, draw the locus of points within triangle ABC which are 4 cm from AB.[1]
Verified working — step 1
Draw a line parallel to AB at a perpendicular distance of 4 cm from it, on the…(b(iii)) On your diagram, draw the locus of points within triangle ABC which are equidistant from AC and BC.[2]
Verified working — step 1
Construct the angle bisector of angle ACB: place the compass point at C, draw arcs cutting CA and CB, then from these arc points dr…(c) A point P, within triangle ABC, is such that it is less than or equal to 7 cm from C, less than or equal to 4 cm from AB and nearer to AC than BC. Indicate, by shading, the region in which P must lie.[2]
Verified working — step 1
On the diagram with all three loci drawn (arc of radius 7 cm from C, line parallel to AB at 4 cm, and bisector of angle C), identify the region that is inside the triangle, on or inside the 7 cm arc from C, on…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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