Year 10 / 11 Mathematics/Constructions & Loci
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?

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Perpendicular bisector of AB