A locus is every point that follows a rule. Describe loci, combine them, and work out lengths and areas of regions.
What you will learn
- Describe the locus of points a fixed distance from a point or a line
- Use the perpendicular and angle bisectors as loci
- Find areas and lengths of regions
Four basic loci
- A fixed distance from a point: a circle.
- A fixed distance from a straight line: two parallel lines (with semicircles round the ends of a segment).
- The same distance from two points: the perpendicular bisector.
- The same distance from two lines: the angle bisector.
"Less than" means the region inside; "at least" means outside. So the locus of points less than 4 cm from P is the inside of a circle of radius 4 cm, centre P, not the circle itself (that is the points exactly 4 cm away). "At most" includes the boundary.
When there are two conditions, the answer is the part that obeys both. Points the same distance from A and B and less than 3 cm from A: the part of the perpendicular bisector of AB that lies inside the circle of radius 3 cm about A.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Four basic loci
- Loci on a grid
- Regions you can measure
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Circle, Parallel lines, Perpendicular bisector, Angle bisector, And, Area of a circle, Circumference
In this unit: Constructions, loci and bearings
Three-figure bearings, scale drawings and maps, ruler-and-compass constructions, and loci: sets of points that follow a rule.