how can i walk throw the line?

see these image:
https://2.bp.blogspot.com/-STOKeDBaa...0/distanc1.png

i know calculate the AB distance using the Pythagorean theorem.
my question is: imagine that i'm on vector A, how can i move, vector a vector, to B?
is just:
X = X + 1
Y = Y + 1
?
and, true, depends on direction.. what i don't know use it..
can anyone explain these to me?
and yes these is a 2D, i need to know, too, in 3D.