Two straight roads PQ and PR 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=100 m locate the position of a flagstaff X, which is equidistant from P and S and is also equidistant from the roads. Measure the distance X from P, and calculate the actual distance (Use ruler and a pair of compasses only).

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520 m

420 m

620 m

500 m

answer is A.

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Detailed Solution

Given, PQ and PR cross each other at P at an angle of

75 °

and S is a stone on the road PQ, 800 m from P, towards Q.
The points on a line's perpendicular bisector are equidistant from the line's endpoints.
Draw a line PQ.
At a distance of 800 metres, mark point S.
PS's right bisector should be drawn.
Create a bisector of angle P.
Make a mark M where X is equally distance from both roads.
Measure the length of PX.
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