If you cast your Graphics object to Graphics2D, you can use the affine transform methods.
For example, scaling by -1.0 in the x-axis might give you a mirror image.
Beware: use the method which copies the Grahpics2D object before using affine transforms. Scale is probably all right, but you can get distortions using shear. Discard the copy after the transforms. I think the copy method is called create().
Moving to our GUIs forum, where we usually discuss such questions.