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.

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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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