In the scale drawing, PQRS represents a plot of land, which is to be used for a park. Scale 1 cm to 0.5 km

- (a)
Find the actual distance between P and Q.
Ans: ___ km
- (b)
Measure the bearing of P from S.
Ans: ___ °
- (c)
Construct the angle bisector of ∠PQR.
- (d)
Construct the perpendicular bisector of RS.
- (e)
A water fountain is to be built in the park, nearer to R than to S and equidistant to PQ and QR. Mark a possible location for the water fountain to be built and label it as F.
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Worked solution
24(c)
1. Construct the angle bisector of $\angle PQR$ using standard compass arcs.
With centre , draw an arc cutting and at two points.
Using the same compass radius from these two points, draw two arcs inside so that they intersect.
Draw a straight line from through the intersection of the two arcs. This line is the angle bisector of .
The angle bisector of is constructed as a straight line from dividing into two equal angles.
24(d)
1. Construct the perpendicular bisector of $RS$ using equal-radius compass arcs.
Set the compass radius to more than half of . With centre , draw arcs above and below . Using the same radius and centre , draw arcs to intersect the first pair of arcs. Draw a straight line through the two arc-intersection points. This line is the perpendicular bisector of .
The perpendicular bisector of is constructed as a straight line crossing at its midpoint at .
24(e)
1. Identify and mark a point satisfying both locus conditions.
Since is equidistant from and , must lie on the angle bisector of .
Since is nearer to than to , must be on the same side of the perpendicular bisector of as .
Choose any point inside the park that lies on the angle bisector of and is on the -side of the perpendicular bisector of . Label this point .
Mark anywhere inside on the angle bisector of , on the side of the perpendicular bisector of nearer to .
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