I believe the OP also needs the direction of the move to be specifically constrained to a line going through *two* arbitrary points (one at the source location, and one at the target).
For that one needs to get used to the (very powerful) "temporary live guide" feature (or whatever it's called :D). To do so :

> Initiate Move
> Make sure that Object Snap is enabled (this can be done before or after the move is initiated)
> while Move is waiting for input, perform a left mouse button "click and drag" input, starting from the first point of reference, and ending at the second point of reference. This creates a reference line anchored to these two points.
> Click on your desired start point (likely one of the two that you defined the direction with)
> With the mouse hovering over the reference line and thus locking the direction of the move, type in the desired distance.