A locus is a set of points satisfying a certain condition. For example, the
locus of points that are 1cm from the origin is a circle of radius 1cm centred
on the origin, since all points on this circle are 1cm from the origin.
N.B. if a point P is
‘equidistant’ from two points A and B, then the distance between P and A is the
same as the distance between P and B, as illustrated here:
The points on the
line are equidistant from A and B
Don’t let the term 'locus' put
you off. Questions on loci (which is the plural of locus) often don’t use the
term.
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.
Copyright © Matthew Pinkney 2003
