Quick Line (just made it up for fun)

Any Two points (and an x and y axis) can form two "Quick" lines (except under three circumstances), can anyone figure out how the lines are determined (you can move the points around)?

hint: My teacher's been making us do things with patty paper.

PS: if you don't have enough information to figure it out, please tell me.

The Two points are the opposite corners of the smallest possible rectangle that touches them. When that rectangle is folded such that the two points lie on top of each other than the line connects the two non-dotted corners

Let's see who's the first to find it. :)