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.
On Nov 2024 Paper 1H (Q2) many drew arcs with centres that were not equidistant from the base point, so the bisector was wrong.
Not using compasses / no construction arcs
Drawing freehand, or a plain line with no arcs, scores nothing even if it looks right.
The most common zero-mark response drew arcs with no clear purpose or sketched freehand arcs (Nov 2024 Paper 1H, Q2).
Rubbing out the construction arcs
Erasing the arcs after drawing the line. The arcs are the EVIDENCE of a correct construction, so rubbing them out throws away the marks even when the line is right.
(general exam technique)
Shading one condition, not the overlap
For a region question, shading a single locus instead of the OVERLAP where every condition holds. Shade only where all the conditions are satisfied at once.
(general exam technique)
Bisector arcs set too small
Setting the compasses to less than half of when drawing a perpendicular bisector, so the two arcs never cross. Open them wider than half first.
(general exam technique)
Keep your construction lines
Never rub out the arcs — they are the evidence the examiner credits.
Same radius for a bisector
Keep the compass width fixed for both arcs of a perpendicular bisector so the crossing points are truly equidistant from and .
Name the locus type first
Identify which of the four standard loci fits — circle, perpendicular bisector, angle bisector or a racetrack of parallel lines with semicircular ends — before you draw.
| 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 from a point?
Describe the locus of all points that are exactly cm from a fixed point .
