Come on, do the Loci-motion..

The word Loci is used to describe lots of things called locus (No! not locusts!).

Locus is another maths word which simply means a set of points under certain conditions - what that's not very clear?

If you think of a locus more of a path which is traced out by something moving, it gets easier to understand.
Imagine you have a dog tied on a fixed length of rope to a post, if the dog runs around the post keeping the rope taut, what will be the locus of the dog's movement?
The answer is......a circle

To see how this works it's easier to look down on the dog and create a model of what's actually going on.

We've labelled the post as point P in the diagram and labelled the length of the rope as x (you can forget the dog now....aaaw).
So, the certain conditions mentioned in the definition earlier are that x is of constant length (the rope is kept taut) and the set of points described by length x from point P (i.e. the locus) is a circle.

 

There are other examples of loci which you need to be aware of, here is one which is often used in examinations to try and catch you out:
Here x is kept constant whilst moving around a rectangle. Note that the locus of x is not as you might at first suspect a larger rectangle, but it is the shape as shown in the diagram. When x turns the corners of the rectangle it actually describes a quarter of a circle.