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Year 11
Higher

Solving loci problems in context

I can solve problems involving a combination of loci.

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New
New
Year 11
Higher

Solving loci problems in context

I can solve problems involving a combination of loci.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Loci problems involve performing various constructions
  2. The problem asks for these constructions within the context of the question
  3. All construction lines should be left on the diagram to show your working

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.

  • 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.

Common misconception

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.

Have pupils design their own loci problems, where multiple different constructions are needed.
Teacher tip

Equipment

Pair of compasses, ruler, protractor, pencil

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which diagram shows an angle bisector?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q2.
Aisha places two cones, A and B, on the ground. Which of these points are closer to A than they are to B?
An image in a quiz
Correct answer: a
c
e
g
Correct answer: h
Q3.
Which of these points are equidistant from ST and TU?
An image in a quiz
a
Correct answer: c
e
g
Correct answer: h
Q4.
Izzy wants to find all the points that are the same distance from LM as they are from MN. What construction should she use?
An image in a quiz
The arc of a circle centred on M
Correct answer: The angle bisector of ∠LMN
The angle bisector of ∠LNM
The angle bisector of ∠NLM
The perpendicular bisectors of MN and LM
Q5.
Which region is illustrated on this diagram?
An image in a quiz
The region of points that are closer to A than to B
Correct answer: 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
Q6.
Select the region which matches this description: closer to AD than CD and closer to AB than BC.
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz

Exit quiz

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6 Questions

Q1.
The locus of points equidistant from another point can be represented by a .
Correct Answer: circle
Q2.
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?
An image in a quiz
A
B
Correct answer: C
D
Q3.
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?
An image in a quiz
Correct answer: A
B
C
Q4.
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?
An image in a quiz
A
Correct answer: B
C
Q5.
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 .
An image in a quiz
Correct Answer: e, E
Q6.
Aisha wants to work out whether point P is closer to point A or point B. What construction should Aisha use?
An image in a quiz
A circle with centre at P.
2 circles with centres at A and B.
Correct answer: A perpendicular bisector between A and B.
A perpendicular between A and B through J.
The angle bisector of angle APB.