Knowledge Organiser: Loci
Part of Loci · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Loci within Loci for GCSE Mathematics. Revise Loci in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 5 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 1 of 1 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 1 of 1
Practice
10 questions
Recall
5 flashcards
Knowledge Organiser: Loci
Key Terms
- Locus (plural: loci): The set of all points satisfying a given condition
- Equidistant: The same distance from two points or lines
- Region: An area satisfying an inequality condition (shade correctly)
- Boundary: The locus line itself — solid if included, dashed if not
Must-Know Loci
- Fixed distance from a point → CIRCLE with that radius
- Equidistant from two points → PERPENDICULAR BISECTOR of the line joining them
- Equidistant from two lines → ANGLE BISECTOR of the angle between them
- Fixed distance from a line → two parallel lines either side (+ semicircles at ends)
- Combinations: sketch each locus, find intersection region
Key Methods
- Read the condition carefully — distance FROM a point or FROM a line?
- Use compasses for circular loci, ruler for straight loci
- Shade the required REGION (not just the boundary)
- Leave construction arcs visible
Key Formulas
- Fixed distance from a point: circle with that radius
- Fixed distance from a line: parallel lines either side
- Equidistant from two points: perpendicular bisector of the line segment
- Equidistant from two lines: angle bisector of the angle between them
Common Mistakes
- Drawing the boundary not the region: Questions often ask for a region — shade the correct side of the boundary
- Distance from a line: The locus is TWO parallel lines (one each side), not a single line
- Erasing arcs: Leave all construction arcs — they show your method and earn method marks
- Misidentifying "equidistant from two lines": Use angle bisector (not perpendicular bisector) when equidistant from two meeting lines
Revise this topic interactively on PrepWise — self-test mode, tap-to-reveal definitions, and Common Mistakes from examiners.
Try the interactive Knowledge Organiser — free →Practice Questions for Loci
Which of the following best defines a locus (plural: loci)?
Explain why the perpendicular bisector of a line segment AB is the locus of all points equidistant from A and B.
Quick Recall Flashcards
10 questions on Loci — practise free
Instant marking, adaptive difficulty, and 5 spaced repetition flashcards. Free until your GCSEs.
Try PrepWise Free