# Fixed Point

## Fixed Point

Element in a plane that is invariant under a given transformation.

A point x in a plane is fixed for a transformation f of the plane if $$f(x)=x$$.

### Example

The centre O of a rotation r is a fixed point, since $$r(O)=O$$.

The centre C of a dilation D is a fixed point for this transformation, since $$D(C)=C$$.