Given two lines in the plane how do I know if there is an orthogonal transformation that maps one into the other?
For example, given two lines $r: (1,2) + \big \langle (1,0) \big \rangle $ and $s: (1,2) + \big \langle (1,1) \big \rangle$ how do I know if there is any rotation ABOUT THE ORIGIN that maps $r$ into $s$?
I know that a clockwise rotation of $45º$ about the point $(1,2)$ would do it, but I am having trouble if the centre has to be the origin. Any hints?