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Bearings, constructions and loci
Bearings give directions as angles. Constructions and loci use a ruler and compasses to draw accurately.
Bearings
A bearing is measured from North, clockwise, and written with three figures: 045°, 210°.
The back bearing (the return journey) is the bearing ± 180°.
The back bearing (the return journey) is the bearing ± 180°.
Constructions
Perpendicular bisector: compass arcs from both ends of a line, then join the crossing points.
Angle bisector: arcs from the vertex, then arcs from those points, join to the vertex.
Never rub out your construction arcs.
Angle bisector: arcs from the vertex, then arcs from those points, join to the vertex.
Never rub out your construction arcs.
Loci
A locus is the set of points that follow a rule.
Fixed distance from a point: a circle.
Equal distance from two points: the perpendicular bisector.
Equal distance from two lines: the angle bisector.
Fixed distance from a point: a circle.
Equal distance from two points: the perpendicular bisector.
Equal distance from two lines: the angle bisector.
The bearing of B from A is 070°. Find the bearing of A from B.
- Back bearing = 070 + 180
Answer: 250°
Bearings: from North, clockwise, three figures; the back bearing is ±180°. Loci: a circle around a point, a perpendicular bisector between two points, an angle bisector between two lines.
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