Question

8(a). Using a ruler and a pair of compasses only, construct:
(i) A quadrilateral PQRS such that |PQ| = 8.5 cm, |QR| = 7.5 cm, ∠QPS = 60°, ∠PQR = 105° and S is a point on the locus L₁ which is equidistant from PQ and QR. Find PQ and QR.
(ii) Locus L₂ of points equidistant from P and Q.
(iii) Locate the point K, which is the point of intersection of L₁ and L₂.
(b) Measure |KS|.

Accepted Answer

(a) Construction steps:
(i) Draw PQ = 8.5 cm. At P construct 60°; at Q construct 105°. Mark R at 7.5 cm from Q. Bisect angle PQR to find L₁.
(ii) Construct perpendicular bisector of PQ → L₂.
(iii) K = intersection of L₁ and L₂.

(b) |KS| = 1.0 cm

WAEC Mathematics 2025 Theory — Question 8

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