NEED HELP! Rotation around a moving point!

Hi MathForum members! I have a problem that I just can't figure out how to solve!(Headbang)
The problem I'm trying to solve is:
I have pollygon with points in a={4,3}, b={3,-1} and c={5,-1} .
Now point a changes to a={sin[t],Sin[2t]}, 0<=t<=2 Pi, but the size of the polygon is still the same! The Pollygon shall move as "a" moves, and the centerline of the pollygon shall allways be in line with the direction of wich the polygon is moving.
How do I rotate b and c to do this?(Headbang)

I hope you understand what I mean! Thx in advance! I really need help!

A drawing or two to illustrate the problem will be very useful.