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Knowledge Organiser: Loci
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
Now try it yourself
Quiz · Question 1 of 10
Which of the following best defines a locus (plural: loci)?
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on loci, with a full worked answer.