ECZ 2020 · O-Level Paper 2 · Question 4 — Construction and Loci
Question from ECZ 2020 · O-Level Paper 2 · Question 4
(a) Construct a quadrilateral PQRS in which PQ = 8 cm, angle QPS = angle PQR = 120 degrees, PS = 6 cm and QR = 5 cm.[1]
Verified working — step 1
Draw PQ = 8 cm, construct 120 degrees at both P and Q, mark PS = 6 cm and QR = …(b) Measure and write the length of RS.[1]
Verified working — step 1
Taking P(0, 0) and Q(8, 0): S = 6(cos 120, sin 120) = (-3, 5.20) and R = Q + 5(cos 60, sin 60) = …(c(i)) Within the quadrilateral PQRS, draw the locus of points which are 4.5 cm from Q.[1]
Verified working — step 1
Set compasses to 4.5 cm with centre Q an…(c(ii)) Within the quadrilateral PQRS, draw the locus of points which are equidistant from P and Q.[1]
Verified working — step 1
Points equidistant from two fixed points lie on the…(c(iii)) Within the quadrilateral PQRS, draw the locus of points which are equidistant from QR and RS.[2]
Verified working — step 1
Points equidistant from two intersecting lines lie on the…(d) A point T, within the quadrilateral PQRS, is such that it is less than or equal to 4.5 cm from Q, nearer to Q than P and nearer to RS than QR. Indicate, by shading, the region in which T must lie.[2]
Verified working — step 1
At most 4.5 cm from Q: inside the arc from (c)(i).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