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Maths

Loci

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# Constructions

## Perpendicular bisector of a line segment

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

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

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

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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