The force the hinge exerts on the trapdoor must have a vertical (up) component (as well as a horizontal right component). Just think if you tried to take moments about the end of the trapdoor where the wire is attached. The COM would be anticlockwise so the hinge must be clockwise.
Apart from that, the other diagrams are not in equilibrium (horizontal/vertical) as the answer says. Just look at the lengths of the arrows.