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

A bearing is an angle measured in degrees from North in the clockwise direction and written with three figures. E.g. an angle of 82° is written as 082°.

The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Advanced problem solving with loci and constructions

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

Solving loci problems in context

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

A {{}} is an angle measured in degrees from North in the clockwise direction and written with three figures.

A boat (B) leaves a port (P) on a bearing of 051° at a speed of 20 km/h. The boat has been travelling for 3 hours and {{ }} minutes.

Three sensors are set up for security. Sensor 1 has a range 15 m, sensor 2 has a range 12 m and sensor 3 has a range 20 m. All 3 sensors are activated. The intruder is likely to be in region {{}}.

angle bisector of angle B$$_{1}$$SB$$_{2}$$

perpendicular bisector of B$$_{1}$$B$$_{2}$$

A ship, S, needs to pass through a point that is midway between two buoys. Which construction can be used to determine the point that the ship must pass through?

A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?

A rear windscreen wiper cleans only part of the glass. The wiper blade is 24 cm long and pivots 160° from the horizontal. The area of the window that is cleaned by the blade is {{ }}π cm².

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

A goat is tied to a railing by a 2 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?

A security 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. Any ship must stay 10 metres of more away from each rock. Which locus shows that are 10 metres away from rock S? (A, C have radii of 10 m).

Sam’s family want to move to a house that is further than 7 km from a factory at P, but also still at most 3 km from the river. Sam's family should move to region {{ }}.

Two mobile phone masts (X and Y) can broadcast their signal to a maximum of 24 km. The further away from the mast, the weaker the signal is.  Which points will not receive a signal from either mast?

Advanced problem solving with loci and constructions

Lesson outcome