need to move my object on a path from a to b( the path is curved) without lifting my mouse button from the object.

I am trying to make a game where I need to move my object on a path from a to b( the path is curved) without lifting my mouse button from the object, if I let go of the mouse button the objects goes back to the original position and i have to start the tracing again. how to trace the object on the path so that the player wins. how to go about it??,I am trying to make a game where I need to move my object on a path from a to b( the path is curved) without lifting my mouse button from the object, if I let go of the mouse button the object goes back to the original position and I have to start the tracing again. how to go about this??