A plane flies at equal distance between two control towers.
The locus of the plane is the perpendicular bisector of the two towers. When a line is divided into two equal lengths, it has been bisected.
Draw the perpendicular bisector of the points X and Y
Draw a line between the points
Place the compass on point X. Open the pair of compasses until it is over halfway along the line. Draw an arc that crosses the line
Place the compass on point Y without changing the width of your compass. Draw another arc that crosses the line
Use a ruler to join the points A and B
The line AB crosses the line XY at a right angle and divides the line XY into two equal lengths
Constructing the bisector of an angle
A path is constructed so it is at equal distance from the two edges of the field, JM and LM
The locus of the path is the angle bisector of the angle LMJ. The path has separated the angle into two equal angles
Bisect the angle V
Place the compass point at V. Draw an arc to cross the two lines
Place the compass point at A. Draw an arc in between the two lines
Place the compass point at B without changing the width of your compass. Draw an arc that crosses the arc from point A
Join the point C to V using a ruler
The angles AVC and BVC are equal
Solving problems using constructions
Problems can involve intersecting loci. It may be necessary to use several constructions to locate a region.
Two lifeboats are searching for a boat in distress. The boat is more than 40 m from the coastal path. It is closer to boat W than boat Z. Shade the region in which the boat lies. Use a scale of 1 cm:10 m
Draw a line parallel to the path 4 cm from the path. Shade in the area which is more than 4 cm from the path
Draw a line between Z and W. Construct the perpendicular bisector of this line. Shade in the region which is closer to W than Z. The boat lies where the two regions overlap