Answer:
The pivot point (or more precisely the "apparent pivot point") is that point along the fore and aft axis of a turning ship, that has no sideways movement, having for reference the surface of the water.
The pivot point is generally at 1/3 ship's length from the bow when the ship is moving ahead, and between ΒΌ ship's length from the stern and the rudder post when going astern. But if a powerful and effective lateral force is applied at one end of the vessel, the position of the pivot point will shift at about 1/3rd ship's length from the other end of the ship (relative to the applied force).