Constructions and loci

Constructions are accurate drawings using a ruler and compasses only. Keep the compass arcs: they show your method. A locus is the set of all points that follow a rule.

Key facts

  • Perpendicular bisector: two arcs the same size from each end, joined where they cross.
  • Angle bisector: arc from the corner, then two equal arcs from where it cut the arms.
  • The locus of points a fixed distance from a point is a circle.
  • Points the same distance from A and B lie on the perpendicular bisector of AB.

Worked examples

Example 1

Construct the perpendicular bisector of a line AB.

  1. Open the compasses to more than half of AB.
  2. Draw an arc above and below from A, then the same from B.
  3. Do the same from B.
  4. Join the two crossing points with a ruler. That line cuts AB in half at right angles.

Answer: A line through the arc crossings