Constructions
- Use a ruler and a pair of compasses, and leave all your construction arcs showing.
- Perpendicular bisector of AB: open the compasses to more than half of AB. Draw arcs from A and from B, above and below the line. Join the two points where the arcs cross.
- Angle bisector: from the corner, draw an arc crossing both arms. From those two points, draw arcs that cross. Join the corner to where they cross.
- Triangle from three sides: draw one side, then set the compasses to each of the other lengths and draw arcs from each end. The arcs cross at the third corner.
Loci
- A locus is a set of points that follow a rule.
- Points a fixed distance from a point make a circle. Points a fixed distance from a line segment make a 'running track' shape: two parallel lines joined by semicircles.
- Points the same distance from two points lie on the perpendicular bisector. Points the same distance from two lines lie on the angle bisector.
Loci problems
- Draw each locus to scale, then shade the region that fits all the rules.
- 'Closer to A than to B' is the side of the perpendicular bisector of AB that contains A.
- 'Less than 3 m from P' is the inside of a circle with centre P and radius 3 m.
Shortest distance
- The shortest distance from a point to a line is the perpendicular distance.
Key terms
- Construction
- An accurate drawing made with a ruler and compasses.
- Perpendicular bisector
- A line that cuts another line in half at right angles.
- Angle bisector
- A line that cuts an angle in half.
- Locus
- A set of points that follow a rule (plural: loci).
- Equidistant
- The same distance from two or more things.
- Perpendicular
- At right angles to.
- Arc
- Part of a circle drawn with compasses.