Mathematics
Two straight roads PQ and PK cross each other at P at an angle of 75°. S is a stone on the road PQ, 800 m from P towards Q. By drawing a figure to scale 1 cm = 100m, locate the position of a flag staff X, which is equidistant from P and S, and is also equidistant from the roads.
Locus
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Answer
Scale given 1 cm = 100m so, 800m = 8 cm.
Two roads PK and PQ are drawn with an angle of 75°.
We know that locus of point equidistant from two lines is the angle bisector between them.
From figure we see that,
PR is the angle bisector of ∠KPQ.
We know that locus of point equidistant from two points is the perpendicular bisector of line segment joining the points.
From figure we see that,
AB is the perpendicular bisector of PS.
AB and PR intersects at X.
Hence, point X is equidistant from P and S also from roads PK and PQ.
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