ECZ 2011 · O-Level Paper 2 · Question 4 — Construction and Loci
Question from ECZ 2011 · O-Level Paper 2 · Question 4
(a(i)) Construct parallelogram ABCD in which AB = 8 cm, BC = 5.3 cm and angle ABC = 60°.[1]
Verified working — step 1
Draw AB = 8 cm.(a(ii)) Construct a perpendicular from A to meet CD at point Q and write down the length of AQ.[2]
Verified working — step 1
AQ is the perpendicular distance between the parallel sides AB and DC.(b) On your diagram, draw the locus of points within the parallelogram ABCD which are
(b(i)) 2.5 cm from AB,[1]
Verified working — step 1
The locus 2.5 cm from the line AB is a line parallel to AB.(b(ii)) 3 cm from C,[1]
Verified working — step 1
The locus 3 cm from C is an …(b(iii)) equidistant from BC and CD.[1]
Verified working — step 1
BC and CD meet at C, so points equidistant …(c) P is a point inside parallelogram ABCD such that P is: nearer to BC than CD, less than or equal to 3 cm from C, less than or equal to 2.5 cm from AB. Indicate clearly, by shading, the region in which P must lie.[2]
Verified working — step 1
Nearer to BC than CD: the BC side of the angle-C bisector.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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