Pass Your GCSE Maths Exams

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.

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.