<image> As shown in the figure, there are three points $$A$$, $$B$$, and $$C$$ on the number line, which can move left and right along the number line. Please answer the following questions: 
$$(1)$$ If point $$B$$ moves three units to the right to point $$D$$, the number represented by point $$D$$ is ______; 
$$(2)$$ Move point $$A$$ to point $$E$$ such that one of the points $$B$$, $$C$$, and $$E$$ is the midpoint of the segment connecting the other two points. Please directly write out the distances and directions of all movements of point $$A$$; 
$$(3)$$ If the three points $$A$$, $$B$$, and $$C$$ move such that they become three distinct rational numbers, and they can be represented in the form of $$1$$, $$a$$, and $$a+b$$, as well as in the form of $$0$$, $$b$$, and $$ \dfrac {b}{a}$$, find the values of $$a$$ and $$b$$.