Rectangle r = path.getBounds();
float x = button.getWidth() / 2 - r.width / 2 + x_offset;
float y = button.getHeight() / 2 - r.height/ 2 + y_offset;

Shape shape = ...
AffineTransform at = AffineTransform.getTranslateInstance(dx, dy);
Shape transformedShape = at.createTransformedShape(shape);