A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.

Two lines are perpendicular if they meet at right angles.

To bisect means to cut or divide an object into two equal parts.

Solving loci problems in context

Maths

Checking and securing understanding of constructing the perpendicular bisector of a line segment

Checking and securing understanding of constructing a perpendicular to a given line through a point

Checking and securing understanding of bisecting an angle

Constructing angles of  90° and 45°

Constructing a triangle given three side lengths using compasses

Constructing a triangle given two side lengths and the angle between them using a compass

Constructing a triangle given two angles and the side length between them

Constructing a right-angled triangle given the length of the hypotenuse and one other side length

Constructing a triangle given two side lengths and an angle not between them

Constructing loci

Applying constructions to loci problems

Problem solving with loci and constructions

The constructions covered in the prior unit are built on in this unit. In this unit, pupils construct triangles and construct diagrams following specific restrictions.

In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.

Loci and construction

The locus of points equidistant from another point can be represented by a {{}}.

A goat is tied to a railing by a 1.5 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?

A door-bell camera (S) can film any object up to 5 metres away. It can only film in locations that it can see in a straight line. Which construction shows the locus of locations the camera can film?

This map shows two rocks, P and S, out at sea. A swimmer swims so that they are always the same distance from each rock. Which locus shows the swimmer's route?

Izzy’s grandma wants to move to a house that is within 7 km of Izzy’s house at P, but also still at most 3 km from the river. Izzy's grandma should move to region {{ }}.

A perpendicular bisector between A and B.

A perpendicular between A and B through J.

Aisha wants to work out whether point P is closer to point A or point B. What construction should Aisha use?

Aisha places two cones, A and B, on the ground. Which of these points are closer to A than they are to B?

Which of these points are equidistant from ST and TU?

Izzy wants to find all the points that are the same distance from LM as they are from MN. What construction should she use?

The region of points that are closer to A than to B

The region of points that are closer to B than to A

The region of points that are equidistant from A and B or closer to A than to B

The region of points that are equidistant from A and B or closer to B than to B

Which region is illustrated on this diagram?

Select the region which matches this description: closer to AD than CD and closer to AB than BC.

Starter Quiz

Which diagram shows an angle bisector?