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
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.
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
Combined Loci
Multiple conditions = find intersection region. Use AND logic. Draw each locus, shade overlap meeting ALL conditions.
Locus from Line
Fixed distance from line = two parallel lines (one each side). Same distance above and below.