# mobius transformation given points

Let P,Q,R ∈ ˆ C be the points P = − √2 + i√2 , Q = 2i , R = √2 + i√2 . Let M : ˆ C→ ˆ C be the Mobius transformation with M(P) = Q , M(Q) = R The points P,Q,R lie on a common hyperbolic line (you do not need to show that). Sketch this line and the line (0,∞) in the upper half plane. Find M(0) and M(∞).