Theory question 112
ConstructionsUsing ruler and a pair of compasses only. (a) construct a quadrilateral PXYQ such that |PX| = 9.9cm, |QX| = 10.2cm, ∠QPX = 75°, |QY| = 10.4cm and PQ//XY. (b) construct the: (i) locus l1 of points equidistant from X and Y, (ii) locus l2 of point equidistant from QY and YX (c) Locate M, the point of intersection of l1 and l2 (d) Measure |PM|.
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(a) Draw PX = 9.9 cm. Construct 75° at P (60° plus half of the 30° between 60° and 90°). With centre X radius 10.2 cm cut this arm at Q (PQ ≈ 6.1 cm). Through X construct a line parallel to PQ; with centre Q radius 10.4 cm cut it at Y. Join QY.
(b)(i) l1: perpendicular bisector of XY.
(ii) l2: bisector of ∠QYX.
(c) M is where l1 and l2 cross.
(d) |PM| ≈ 9.5 cm (accept 9.3–9.7 cm).
Equidistant from two points: perpendicular bisector. Equidistant from two lines: angle bisector.