Constructions and Loci
Geometric constructions use a compass and ruler to draw accurate shapes, and a locus is the path of points obeying a rule.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Geometric constructions use a compass and ruler to draw accurate shapes, and a locus is the path of points obeying a rule.
- Bisect an angle with arcs
- The perpendicular bisector is equidistant from two points
- A circle is the locus of points at a fixed distance
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Constructions and Loci?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Constructions and Loci. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Constructions and Loci in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Constructions and Loci gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Constructions and Loci in detail
Constructions use a compass and straight edge to draw accurate geometric figures without measuring: the perpendicular bisector of a line, the bisector of an angle, a perpendicular from a point to a line and triangles from given sides. Construction arcs must be left visible.
A locus is the set of all points that satisfy a given rule, such as all points a fixed distance from a point (a circle) or equidistant from two points (a perpendicular bisector). Combining loci lets you shade regions, for example the area within 5 m of a tree and closer to one fence than another. These skills are used in design, engineering and mapping.
How the interactive helps you understand Constructions and Loci
Watch the circle in the interactive. Use any sliders or buttons it offers to change the values and see how the circle responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Constructions and Loci.
Real-life uses and examples
- Explain Constructions and Loci to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Constructions and Loci in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Constructions and Loci by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Constructions and Loci without checking why they work.
- Forgetting units, signs or brackets when you apply Constructions and Loci.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Constructions and Loci
What is Constructions and Loci?
Geometric constructions use a compass and ruler to draw accurate shapes, and a locus is the path of points obeying a rule.
What are the most important points about Constructions and Loci?
The main points are: Bisect an angle with arcs; The perpendicular bisector is equidistant from two points; A circle is the locus of points at a fixed distance.
Why is Constructions and Loci useful?
Understanding Constructions and Loci gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Constructions and Loci?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Constructions and Loci?
Related topics in Mathematics include Independent and Mutually Exclusive Events, Range and Spread, Pie Charts.