Key Points

A locus is a line that is always the same distance from another line, or point.

A circle is a locus from a point (centre)

In constructing accurate locus, a compass is your best friend!

 

Draw a line equidistant from two points.

Suppose we have Point A and Point B.

We draw a semi-circle with a compass, one with your point at A and your pencil at B.
We do the same twith your point at B and your pencil at A.
They will meet at 2 points.
Draw a line, using a ruler, connecting them to get your equidistant line.

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Bisect an angle.

To construct this, we want to 'bisect the angle' which means split the angle in to two equal halves, which would give a line that is equidistant to both the black line and the red line.

We use a compass to do this.

Draw an arc from the angle at O that crosses both lines.
Where it crosses these lines we shall label it C and D.
Place your compass, without changing its size, so that the point is on C and draw an arc
Do the same with the point on D. 
Where these two arc's meet, draw a line with a ruler connecting it to O.
You know have bisected the angle and drawn an equidstant line.

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You will be expected to be able to construct a range of standard loci, as well build loci for unfamiliar shapes, based on the rules you know.

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