ECZ 2022 · GCE Paper 2 · Question 5 — Construction and Loci
Construction on plain paper: triangle KLM.
(a(i)) Construct triangle KLM in which KL = 11cm, angle MKL = 70° and angle KLM = 50°.[1]
Verified working — step 1
Draw line KL = 11 cm using a ruler. At K, use a protractor to construct angle MKL = 70°. At L, construct angle KLM = …(a(ii)) Measure and write the length of LM.[1]
Verified working — step 1
Using a ruler, measure the length of LM o…(b(i)) Construct the locus of points equidistant from K and L.[1]
Verified working — step 1
With centre K and radius more than half of KL, draw an arc above and below KL. Repeat with centre L using the same radius so the arcs intersect above and…(b(ii)) Construct the locus of points 3cm from KL.[1]
Verified working — step 1
Draw a line parallel to KL at a perpendicular distance of 3 cm on the side of M (inside the triangle) and, if required, another parallel…(b(iii)) Construct the locus of points 8cm from K.[1]
Verified working — step 1
With centre K and radius 8 cm, draw an arc (or full circle) usin…(c) A point X within triangle KLM is such that it is 3cm from KL and 8cm from K. Label the point X.[1]
Verified working — step 1
On the diagram, find where the 3 cm-from-KL locus (parallel line drawn in b(ii), inside the triangle) cr…(d) Another point Y is such that it is nearer to L than K, greater than or equal to 3cm from KL and less than or equal to 8cm from K. Indicate clearly, by shading, the region in which Y must lie.[2]
Verified working — step 1
Y must satisfy three conditions simultaneously: (1) on the L-side of the perpendicular bisector of KL (nearer to L), (2) on or beyond the 3 cm parallel line from KL (distance ≥ 3 cm from KL, i.e. away from KL), (3) within or on the 8 cm circle centred …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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