In: Advanced Math
Let x = (1,1) and y = (3,1).
1. Find an explicit hyperbolic isometry f that sends the semicircle that x and y lie on to the positive part of the imaginary axis. Write f as a composition of horizontal translations, scalings, and inversions.
2. Compute f(x) and f(y).
3. Compute d_{H^2}(f(x),f(y)) and verify that f is an isometry.