Problem solving with loci and constructions | Maths | Quizalize & Oak National Academy

Starter quiz

The locus of points __________ from another point can be represented by a circle.

bisecting

equidistant ✓

parallel

perpendicular
A goat is tied to a railing by a 1 metre long rope. There is a barn near the railing. Which of these shows the locus of points the goat can walk to?

A ✓

B

C

D
A motion sensor (S) can film any object up to 5 metres away. It can only detect in locations that it can see in a straight line. Which construction shows the locus of locations the sensor can detect?

A

B

C ✓
This map shows two rocks, P and S, out at sea. Any ship must stay 10 metres or more away from each rock. Which locus shows points that are all 10 metres away from rock P? (A, C have radii of 10 m).

A ✓

B

C
Laura’s grandma wants to move to a house that is within 7 km of Laura’s house at P, but more than 3 km from the river. Laura's grandma should move to region ______.

'c' ✓
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 receive a signal from both masts?

A

D ✓

E

F

G ✓

Exit quiz

A bearing is an angle measured in degrees from __________ in the clockwise direction and written with three figures.

East

North ✓

South

West
A boat (B) leaves a port (P) on a bearing of 047° at a speed of 20 km/h. The boat has been travelling for ______ hours.

'4' ✓
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. Sensors 2 and 3 are activated. The intruder is likely to be in region ______.

'D' ✓
A ship, S, needs to pass through a point that is midway between two buoys. Alex and Sam both do some constructions to find the correct point to pass through. Whose construction is correct?
A ship, S, needs to pass through a point that is midway between two buoys. What bearing should the ship sail on?

20°

020°

160° ✓

240°
A goat is tethered to a horizontal pole by a rope with a ring attached. The pole is 5 metres long and the rope is 3 metres long. What is the area of region that the goat can graze?

3(12π + 5) m²

6(6π + 5) m²

3(3π + 5) m²

3(3π + 10) m² ✓

Worksheet

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Lesson Details

Key learning points

Your knowledge of loci can be applied to your knowledge of bearings
Your knowledge of loci can be used to help solve area problems

Common misconception

Pupils may not consider that, in some contexts (e.g. a corded lawnmower), the shape of the locus will include sectors of different radii, if a shape/object is creating a barrier.

Have pupils consider the impact of going around the corner of a shape.

Keywords

Locus/loci - A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.
Bearing - 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°.
Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.