ECZ 2013 · O-Level Paper 2 · Question 6 — Construction and Loci
Question from ECZ 2013 · O-Level Paper 2 · Question 6
(a) Construct a quadrilateral KFML in which KL = 8 cm, KF = 4 cm, LM = 9 cm, angle FKL = 62° and angle KLM = 118°. Measure and write the length FM.[2]
Verified working — step 1
Draw KL = 8 cm.(b) Inside the quadrilateral KFML, draw the locus of points which are:
(b(i)) 4 cm from L,[1]
Verified working — step 1
The locus 4 cm from L is an …(b(ii)) 3 cm from KL,[1]
Verified working — step 1
The locus 3 cm from the line KL is a line parallel to KL.(b(iii)) equidistant from MF and ML.[1]
Verified working — step 1
MF and ML meet at M, so points equidistant …(c) Given that P is a point inside the quadrilateral such that it is 4 cm from L, more than 3 cm from KL and equidistant from MF and ML, label point P.[1]
Verified working — step 1
P must satisfy all three conditions.(d) Another point Q inside the quadrilateral is such that it is more than 3 cm from KL, less than 4 cm from L and nearer to MF than to ML. Indicate, by shading, the region in which Q must lie.[2]
Verified working — step 1
More than 3 cm from KL: beyond the parallel from (b)(ii), away from 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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question