Constructions: bisecting lines and angles

Constructing a perpendicular bisector

A plane flies at equal distance between two control towers.

Plane following a locus line, 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.

Example

Line between points X & Y

Draw the perpendicular bisector of the points X and Y

Constructing the bisector of an angle

Example 1

Field marked out with points J, L & M

A path is constructed so it is at equal distance from the two edges of the field, JM and LM

Example 2

2 lines coming out from point V

Bisect the angle V

Solving problems using constructions

Problems can involve intersecting loci. It may be necessary to use several constructions to locate a region.

Example

Two lifeboats, W & Z

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