---
title: "Constructions and Loci"
description: "Construct perpendicular bisectors, angle bisectors and perpendiculars with compasses, and shade the region that fits a set of distance conditions."
canonical: https://lightmysky.com/learn/mathematics/constructions-and-loci-mt_yqoXwrKaW3
source: https://lightmysky.com/learn/mathematics/constructions-and-loci-mt_yqoXwrKaW3.md
retrieved: 2026-09-12
---

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# Constructions and Loci

Construct perpendicular bisectors, angle bisectors and perpendiculars with compasses, and shade the region that fits a set of distance conditions.

Subject: Mathematics · Area: Geometry · Ages 15 to 16
Page: https://lightmysky.com/learn/mathematics/constructions-and-loci-mt_yqoXwrKaW3

## Ready when they can

- Construct a perpendicular bisector and an angle bisector, leaving the arcs visible
- Describe the locus of points a fixed distance from a line segment
- Shade the region that satisfies two conditions at once

## Lesson: Bisectors, loci and shading regions

To bisect an angle, swing one arc across both arms from the vertex, then two matching arcs from those crossings. Keep the compass width fixed throughout. An 80 degree angle splits into two 40 degree angles.

**Example.** A perpendicular bisector cuts a segment in half at right angles. Open the compass wider than half, arc from each end above and below, then join the crossings. For A(2, 4) and B(6, 8) the midpoint is (4, 6). Leave every arc visible for method marks.

A locus is the set of points fitting a distance rule. Points exactly 3 cm from P make a circle of radius 3. Points within 3 cm of a line make a 6 cm wide strip. Points a fixed distance from a segment make a stadium: a rectangle with semicircles on the ends.

**Tip.** For two conditions at once, draw each region, then shade only their overlap. Points closer than 5 cm to P and on the same side of a line as Q sit in the overlap of the disc and the half plane.

**Recap.** Bisect with steady compass arcs, read loci as distance rules, and shade only the overlap of all conditions.

## Practice

17 questions on this page, each with its working shown.