Constructions, loci and bearings
Standard constructions (compass + straight edge only)
CCEA awards a mark for showing arcs — never erase your construction marks.
Perpendicular bisector of AB
- Compass set to more than half AB.
- Arcs from A and from B (both above and below).
- Join intersection points with a straight line.
Angle bisector of ∠ABC
- Arc centred at B cuts BA and BC.
- From those two intersections, equal-radius arcs cross.
- Join B to the crossing point.
Perpendicular from a point to a line (P not on line)
- Arc centred at P cuts the line at two points X, Y.
- From X and Y, equal-radius arcs cross below.
- Join P to that crossing.
60° angle (and equilateral triangle)
- Arc from A through B (radius AB).
- Same radius from B; the two arcs meet at C.
- Triangle ABC is equilateral.
Loci
A locus is a set of all points that satisfy a rule.
| Locus | Construction |
|---|---|
| Distance r from point P | Circle, centre P, radius r |
| Equidistant from A and B | Perpendicular bisector of AB |
| Equidistant from two lines | Angle bisector of the angle between them |
| Distance d from a line | Two parallel lines at distance d, joined by semicircles at each end |
Bearings
Bearings are angles measured clockwise from north as a 3-digit number (e.g. 045°, 270°).
To find a bearing:
- Draw a north line at the start point.
- Measure clockwise to the destination.
- Always 3 digits — write 052°, not 52°.
To find the back-bearing:
- If less than 180°, add 180°.
- If 180° or more, subtract 180°.
- Bearing of A from B = bearing of B from A ± 180°.
Common CCEA exam tip
When asked to "construct" using ruler and compasses, leave construction arcs visible — they earn the M1 method mark. A perfectly drawn line with no arcs scores zero.
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