The correct answer is A) the geometric center of the displaced volume. In the absence of external forces, the center of gravity of a floating vessel is located directly in line with the geometric center of the displaced volume. This is because the buoyant force, which acts upward through the geometric center of the displaced volume, must be equal and opposite to the gravitational force, which acts downward through the center of gravity, in order to maintain the vessel's equilibrium in the water. The other options are incorrect because: B) amidships refers to the midpoint of the vessel's length, not the center of gravity; C) the metacenter is a different point related to the vessel's stability; and D) the center of flotation is the point about which the waterplane area rotates, not the center of gravity.