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Maths

Loci

Constructions

Perpendicular bisector of a line segment

image: right angle degree

The locus of a point which moves so that it is an equal distance from two points, A and B, is the perpendicular bisector of the line joining A and B.

Perpendicular means at right angles to.

Bisector means cuts in half.

To construct this locus, you do the following (try this yourself on a piece of paper):

Perpendicular bisector of a line segment

image: bisect a line segment, stage 1

Draw the line segment XY.

Practise this construction until you can do it without looking at the instructions. You don't need to label the points with letters each time - they are just there as a guide.

Bisecting an angle

To bisect an angle, you do the following:

Bisecting an angle

image:bisect an angle, stage 1

V is the vertex of the angle we want to bisect.

Try this yourself on a piece of paper.

Remember: if you are asked to do a construction in an exam, do not rub out your construction lines.

Equal distance from two lines

image: five point dots

The loci of a point which moves so that it is the same distance from lines AOB and COD, are the lines which bisect angles AOC, AOD, DOB and BOC:

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