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A locus is the set of points satisfying a rule, such as a fixed distance from a point or line. This topic covers accurate ruler-and-compass constructions and loci to solve region problems. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Use compasses, not measurement. A fixed distance from a point gives a circle; from a line, a pair of parallel lines with rounded ends. Equidistant from two points is the perpendicular bisector; from two lines, the angle bisector. Leave the construction arcs visible.
Before you start
You need angle facts and compass work before this makes sense. Assessed at Foundation and Higher tier. Later work on geometric reasoning assumes it. Filed under Geometry.
What you learn
A locus is the set of all points that obey a rule — for example, ‘always 3 cm from a point’. Many loci are built using ruler-and-compass constructions. The perpendicular bisector of AB is built with equal arcs from A and from B. The locus of points a fixed distance r from a point P is a circle of radius r, centre P. Points that are equidistant from two lines lie on the angle bisector of the angle between them. The course works through two key constructions, loci: distance from a point or a line and equidistant from two lines, and regions. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our GCSE maths courses, Loci & Construction belongs to Geometry and is met in Foundation tier. There are 3 teaching sections and 2 fully worked examples, plus 3 sets of check questions. It sits alongside Pythagoras' Theorem, Sine & Cosine Rule and Transformations in the same strand. You can drill this strand further on the Geometry revision engine, with your accuracy saved to your skill tree.
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