Ever wondered what shape a tethered goat can graze?
Zainab ties her goat to a post with a 4 m rope. With the rope pulled tight, the goat walks round and round — and traces a perfect shape on the grass. That path is a locus.
Revision notes
Describe the path of points that follow a rule: circles, perpendicular bisectors, angle bisectors and parallel lines.
Zainab ties her goat to a post with a 4 m rope. With the rope pulled tight, the goat walks round and round — and traces a perfect shape on the grass. That path is a locus.
A locus (plural loci) is the set of all the points that obey a rule, or the path traced by a point moving by a rule.
Fixed distance from one point: a circle with that point as centre. The goat on a 4 m rope traces a circle of radius 4 m (diameter 8 m).
Same distance from two points A and B: the perpendicular bisector of AB. A borehole equally far from two houses must lie on it.
🔑 Key idea: One point + fixed distance → circle. Two points + equal distance → perpendicular bisector.
Fixed distance from a straight line: a pair of parallel lines, one on each side. Points 3 cm from a line give two lines 6 cm apart.
Same distance from two parallel lines: one line halfway between them.
Same distance from two lines that meet: the bisector of the angle between them.
🔑 Key idea: Fixed distance from a line → two parallel lines. Equal distance from two meeting lines → angle bisector.
Use your constructions: a circle with the compasses; the perpendicular bisector (arcs from A and B); the angle bisector (arcs from the vertex, then from the arms).
Always ask two questions: is it a fixed distance or an equal distance? And is it from points or from lines?
🔑 Key idea: Fixed or equal? Points or lines? The answers tell you which locus to draw.
The locus of points exactly 5 cm from a straight line l is a pair of parallel lines. How far apart are these two lines?
Step 1: One on each side
5 + 5 = 10 cm
Answer: 10 cm
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.