Loci & Constructions

A locus is a set of points satisfying a certain condition. The term ‘locus’, however, is rarely used in exams. The question is more likely to be of this format:

Example:
The diagram shows two points P and Q. On the diagram shade the region which contains all the points which satisfy both the following: the distance from P is less than 3cm, the distance from P is greater than the distance from Q.

loci-h8

All of the points on the circumference of the circle are 3cm from P. Therefore all of the points satisfying the condition that the distance from P is less than 3cm are in the circle.
If we draw a line in the middle of P and Q, all of the points on this line will be the same distance from P as they are from Q. They will be therefore closer to Q, and further away from P, if they are on the right of such a line.
Therefore all of the points satisfying both of these conditions are shaded in red.