New
New
Lesson 10 of 13
New
New
- Year 11
Constructing loci
I can construct a set of points that satisfy a set of conditions.
Lesson details
Key learning points
- Constructing a set of points a set distance from a given point produces a circle
- A compass should be used for this construction
- The point could be the vertex of a shape or contained within a shape
- A ruler should be used to indicate two points that are a set distance from a line
- The end points of the line should have a compass used to indicate the distance from the point
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.
Circle - A circle is a locus of points that are equidistant from a fixed point. This fixed point is the centre of the circle and the distance from the centre to the locus of points is the radius of the circle.
Common misconception
Pupils may think that the locus of a line is a rectangle.
Choose the vertices of their rectangle and ask if they are the same distance from the line as another point. Link to Pythagoras' theorem if necessary to highlight that the diagonal length will be longer.
If possible, have your pupils organise themselves to construct a locus (similar to the examples in the lesson), or use counters.
Teacher tip
Equipment
Ruler, pair of compasses, pencil
Licence
This content is © Oak National Academy Limited (2025), 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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Prior knowledge starter quiz
6 Questions
Q1.Which angle is 52°?
Which angle is 52°?
∠PQR
∠PRQ
Q2.Match the tools with what they are useful for when constructing a triangle.
Match the tools with what they are useful for when constructing a triangle.
Q3.Match each triangle to the type of triangle it is.
Match each triangle to the type of triangle it is.
Q4.Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join B to?
Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join B to?
C only
D only
Midpoint of C and D
Q5.The following information is given for five different triangles. Jun and Sam both accurately construct each triangle. Which triangle information may not produce 2 congruent triangles?
The following information is given for five different triangles. Jun and Sam both accurately construct each triangle. Which triangle information may not produce 2 congruent triangles?
Triangle 1: ASA
Triangle 2: RHS
Triangle 3: SAS
Triangle 5: SSS
Q6.Match each step to the correct instruction in order to construct the triangle PQR.
Match each step to the correct instruction in order to construct the triangle PQR.
Assessment exit quiz
6 Questions
Q1.A is a set of points that satisfy a given set of conditions.
A is a set of points that satisfy a given set of conditions.
Q2.Which diagram shows the locus of points exactly 2 metres from point P?
Which diagram shows the locus of points exactly 2 metres from point P?
Diagram b
Diagram c
Diagram d
Q3.Which diagram shows the locus of points less than 2 metres from point P?
Which diagram shows the locus of points less than 2 metres from point P?
Diagram a
Diagram b
Diagram d
Q4.Which diagram shows the locus of points 5 metres or more from the line segment PQ?
Which diagram shows the locus of points 5 metres or more from the line segment PQ?
Diagram a
Diagram c
Diagram d
Q5.Which diagram shows the locus of points less than 5 metres from the line segment PQ?
Which diagram shows the locus of points less than 5 metres from the line segment PQ?
Diagram a
Diagram b
Diagram c
Q6.Izzy stands somewhere in her garden. Izzy is less than 5 m from the house and less than 6 m from the tap. She is within 3 m of the tree. Izzy is standing in region .
Izzy stands somewhere in her garden. Izzy is less than 5 m from the house and less than 6 m from the tap. She is within 3 m of the tree. Izzy is standing in region .
