Let x = (1,1) and y = (3,1). 1. Find an explicit hyperbolic isometry f that...

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.

Expert Solution

Colby Messinger answered 2 years ago

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