Constructing loci
I can construct a set of points that satisfy a set of conditions.
Constructing loci
I can construct a set of points that satisfy a set of conditions.
These resources will be removed by end of Summer Term 2025.
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.
Equipment
Ruler, pair of compasses, 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
6 Questions
Finding all possible positions for a vertex when drawing a 2nd side
Drawing an angle to show what direction a side takes
Drawing the first side of a triangle
RHS
SAS
SSA
ASA
SSS
Use a ruler to draw side PQ.
Set compasses to 7 cm and draw a circle centre Q.
Draw a ray line at angle of 45° at P.
Mark R at the point(s) where the ray and circle meet.
Add the line(s) RQ to complete the triangle(s).
Exit quiz
6 Questions
