Q2. Let HCC be the upper half plane with the hyperbolic metric (the Hyperbolic Plane). (i) [6 marks] Prove than any matrix ME SL(2, R) representing a Möbius transformation is an isometry of H. (ii) [6 marks] Prove that the positive y-axis is a geodesic of the Hyper- bolic Plane. (iii) [6 marks] Let y denote the positive y-axis and let p = (1, 2). Find two geodesics of the Hyperbolic Plane containing p that do not intersect (iv) [7 marks] Find the area of the hyperbolic (geodesic) triangle with vertices (0,0), (1, 0) and (0, 1).