Theory question 108
Constructions(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. (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|
Show the model answer
Model answer
(a)(i) Draw PQ = 8.5 cm; construct ∠PQR = 105° (90° + 15°) and mark QR = 7.5 cm; construct ∠QPS = 60° at P
L1 is the bisector of ∠PQR; S is where it meets the 60° arm from P; join RS
(ii) L2 is the perpendicular bisector of PQ
(iii) K is where L2 meets L1
(b) |KS| ≈ 1.0 cm (accept 0.9 – 1.1 cm)
Explanation
Points equidistant from two lines lie on the bisector of the angle between them.