Unit 2 – Geometry · Both
Constructions & Loci
Standard ruler-and-compass constructions and loci (sets of points satisfying a rule).
You must be able to construct perpendicular bisectors, angle bisectors and simple loci with ruler and compasses – and describe loci in words.
Standard constructions
• **Perpendicular bisector** of a line segment – all points equidistant from two endpoints
• **Angle bisector** – all points equidistant from two rays/lines
• Perpendicular from a point to a line
• Equilateral triangle / 60° angle
Leave construction arcs visible in the exam.
Loci
A **locus** is a set of points that satisfy a condition.
• Fixed distance from a point → **circle**
• Fixed distance from a line → **parallel lines** (two sides)
• Equidistant from two points → **perpendicular bisector**
• Equidistant from two lines → **angle bisector**
• Combined regions – shade the region that meets all conditions
Practice questions
Try these without looking at the answers first.
Q1.Locus of points 3 cm from a fixed point?
Show answer
Circle radius 3 cm
Q2.Locus of points equidistant from A and B?
Show answer
Perpendicular bisector of AB