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Maths

Loci

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A locus is a path. The path is formed by a point which moves according to some rule.

The plural of locus is loci.

Simple loci

Example The locus of a point moves so that it is always a set distance (x) from a fixed point (O). What shape is it?

Imagine the minute hand on a clock. As the hand moves around the clock face, think of the path it follows.

Remember: the easiest way to draw this locus around a set point is to use a compass.

Example The locus of a point moves so that it is always a set distance (r) from the line between the points P and Q.

What shape is it?

The straight lines of the locus are parallel to the line from P to Q, because they are at a set distance (r) from the line. P and Q are fixed points at either end of the line, so we draw semicircles of radius r.

Sometimes the locus is not just a line, but an area. For example:

A cow grazing in the field ABCD moves so that it is always a distance of 5m from fence AB. Draw the locus of the cow.

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