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A locus is simply a set of points that satisfy some sort of condition. Here are some common loci that you need to be able to draw...

The set of points, which are the same distance from a single point, is a circle.

For example: Use a pair of compasses. Draw the locus of points that is 5cm away from the cross marked.


The set of points that are the same distance from two points is a perpendicular line straight down the middle! You can draw this by finding the middle with your ruler then drawing a line at 900 or you cantry this clever way just using compasses:

1. Set your compasses so that they are roughly the same as the distance between the points (or less if you don't have a lot of room!).

2. Put the point of the compasses on the first cross and do two arcs - one above the points and one below.

3. Put the point on the second cross and do the same thing so that you cross the first arcs (making sure you keep the compasses the same distance apart).

4. Now simply draw a line straight down the middle through the points where the arcs cross.

Note: Don't rub the arcs out, so the examiners will be able to see what you've done!

Click 'Show Me' below and the diagram will show you each step:

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When two lines meet, you get an angle. The set of points that are the same distance away from both lines is a straight line down the middle which bisects (cuts in half) the angle. Again, you could draw this line down the middle by using a protractor to measure the angle and halve it but, yes you've guessed it, there's a clever way!

1. Get a pair of compasses and place the point where the two lines meet. Draw little arcs that cross each of the lines.

2. Now, keeping the compasses set, put the point on each line where your arc has crossed it and draw another little arc in-between the two lines. You should now have another two little arcs in the middle.

3. Draw a straight line from the angle through the point where your little arcs cross and you've done it!

Confused? Click 'Show Me' below and the diagram will show you each step:

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