Year 11 - Maths
Constructing loci
Loci and construction
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.
Lesson Summary
You will learn to construct a set of points that satisfy a set of conditions.
Key Notes
- 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
Vocabulary To Learn
- 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 Mistakes To Avoid
- Pupils may think that the locus of a line is a rectangle.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Constructing a set of points a set distance from a given point produces a circle. A compass should be used for this construction.
2. Use this key word in a maths sentence and explain it clearly. '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. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think that the locus of a line is a rectangle. Correction: 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.
More Lessons In This Unit
- Advanced problem solving with loci and constructions Study Guide
- Applying constructions to loci problems Study Guide
- Checking and securing understanding of bisecting an angle Study Guide
- Checking and securing understanding of constructing a perpendicular to a given line through a point Study Guide
- Checking and securing understanding of constructing the perpendicular bisector of a line segment Study Guide
- Constructing a right-angled triangle given the length of the hypotenuse and one other side length Study Guide
- Constructing a triangle given three side lengths using compasses Study Guide
- Constructing a triangle given two angles and the side length between them Study Guide
- Constructing a triangle given two side lengths and an angle not between them Study Guide
- Constructing a triangle given two side lengths and the angle between them using a compass Study Guide
- Constructing angles of 90° and 45° Study Guide
- Problem solving with loci and constructions Study Guide
- Solving loci problems in context Study Guide
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