In this scale drawing, A, B and C are three corners of a park ABCD with C due north of B.

- (a)
Construct the perpendicular bisector of BC.
- (b)
D is on a bearing of 065° from A and equidistant from B and C.
Mark and label point D on the drawing.
- (c)
Construct the bisector of angle ABC.
- (d)
Eleanor is standing inside the park ABCD such that she is closer to BC than AB and closer to B than C.
Shade the region where Eleanor could be standing.
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Worked solution
22(a)
1. Construct the perpendicular bisector of $BC$ accurately.
Set the compass radius to more than half of . With centre , draw arcs on both sides of . Using the same radius with centre , draw arcs to intersect the first pair of arcs. Join the two arc intersection points with a straight line.
This line is the perpendicular bisector of .
The perpendicular bisector of is constructed: a straight line crossing at and passing through the midpoint of .
22(b)
1. Draw the locus satisfying the bearing condition from $A$.
From , draw a north line. Measure a clockwise angle of from north and draw the ray from on this bearing.
2. Use the equidistant condition to locate and label $D$.
Since is equidistant from and , lies on the perpendicular bisector of constructed in part (a). Mark the intersection of the bearing ray from with this perpendicular bisector and label it .
Point is marked and labelled at the intersection of the bearing line from and the perpendicular bisector of .
22(c)
1. Construct the angle bisector of $\angle ABC$ accurately.
Using a compass, draw an arc centred at to cut and . From the two intersection points, draw equal-radius arcs to meet inside . Draw a straight line from through the intersection of these arcs. This line is the bisector of .
The bisector of angle is constructed: a straight line/ray from that divides into two equal angles.
22(d)
1. Identify the two locus boundaries and choose the correct side of each boundary.
Points closer to line than to line lie on the side of the angle bisector of .
Points closer to than to lie on the side of the perpendicular bisector of .
Therefore, shade the intersection of these two half-regions inside the park .
Shade the region inside that is on the side of the angle bisector of and on the side of the perpendicular bisector of .
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