Solving loci problems in context | Maths | Quizalize & Oak National Academy

Starter quiz

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

a ✓

c

e

g

h ✓
Which of these points are equidistant from ST and TU?

a

c ✓

e

g

h ✓
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 arc of a circle centred on M

The angle bisector of ∠LMN ✓

The angle bisector of ∠LNM

The angle bisector of ∠NLM

The perpendicular bisectors of MN and LM
Which region is illustrated on this diagram?

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

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

'circle' ✓
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

B

C ✓

D
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?

A ✓

B

C
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?

A

B ✓

C
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 ______.

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

A circle with centre at P.

2 circles with centres at A and B.

A perpendicular bisector between A and B. ✓

A perpendicular between A and B through J.

The angle bisector of angle APB.

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Pupils may erase their construction marks.

Remind pupils that they should always leave their construction marks on their diagrams but encourage them not to press to hard with their pencils.

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.
Perpendicular - Two lines are perpendicular if they meet at right angles.
Bisect - To bisect means to cut or divide an object into two equal parts.