Mathematics
Using ruler and compasses only, construct a parallelogram ABCD in which AB = 5.1 cm, diagonal AC = 5.6 cm and diagonal BD = 7 cm. Locate the point P on DC, which is equidistant from AB and BC.
Locus
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Answer
Steps of construction :
Draw AB = 5.1 cm as base.
At A, with radius 2.8 cm and at B with radius 3.5 cm draw two arcs intersecting each other at O.
Join AO and produce it till C such that OC = AO = 2.8 cm and join BO and produce it till D such that OD = BO = 3.5 cm.
Join A, B, C and D forming parallelogram ABCD.
We know that locus of point equidistant from two lines is the angle bisector of the two lines.
From figure,
BE is the angle bisector of ∠ABC which meets DC at P.
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