Four standard loci
Fixed distance from a point → a circle; equidistant from two points → the perpendicular bisector; equidistant from two lines → the angle bisector; fixed distance from a line → a "racetrack" of parallel lines and semicircular ends.
Use compasses and leave the arcs
Constructions must be done with a pair of compasses, and the construction arcs must be left visible as evidence.
Drawn from real examiner reports.
Drawing arcs from the wrong centres
For an angle bisector the arcs must come from points equidistant from the vertex, not from arbitrary points.
Not using compasses / no construction arcs
Drawing freehand, or a plain line with no arcs, scores nothing even if it looks right.
Keep your construction lines
Never rub out the arcs — they are the evidence the examiner credits.
| Condition | Locus |
|---|---|
| A fixed distance from a point | a circle, radius , centre |
| Equidistant from two points , | the perpendicular bisector of |
| Equidistant from two lines | the angle bisector |
| A fixed distance from a line segment | two parallel lines with semicircular ends |
Locus of points a fixed distance d from a single point P — what shape, and how do you draw it?
Describe the locus of all points that are exactly cm from a fixed point .
