Prove that the only invariant point in a nonidentity dilation with center C is C itself.
I'm not sure where to start to prove this...but by definition of a dilation it seems like it should not be all that difficult...
The distance of any point to the center will be a scale factor of it's original distance if you compare before the dilation and after the dilation. That means the point moved. The only point that this doesn't happen to is the center, because the distance was originally 0.