ECZ 2022 · GCE Paper 2 · Question 5 — Construction and Loci
Answer the whole of this question on a sheet of plain paper.
(a(i)) Construct triangle KLM in which KL = 11 cm, angle LKM = 70° and angle KLM = 50°.[1]
Verified working — step 1
Draw KL = 11 cm.(a(ii)) Measure and write the length of LM.[1]
Verified working — step 1
Measure LM with a ruler on the finished construction: LM = …(b) On your diagram, within triangle KLM, construct the locus of points that are
(b(i)) equidistant from K and L,[1]
Verified working — step 1
Points equidistant from K and L lie …(b(ii)) 3 cm from KL,[1]
Verified working — step 1
The locus 3 cm from the line KL is a line…(b(iii)) 8 cm from K.[1]
Verified working — step 1
The locus 8 cm from the point K is a…(c) A point X within triangle KLM is such that it is 3 cm from KL and 8 cm from K. Label the point X.[1]
Verified working — step 1
X satisfies bot…(d) Another point Y is such that it is nearer to L than K, greater than or equal to 3 cm from KL and less than or equal to 8 cm from K. Indicate clearly, by shading, the region in which Y must lie.[2]
Verified working — step 1
Nearer to L than K: the L side of the perpendicular bisector of KL.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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