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#3)Consider the asymptotic triangle with vertices (0, 1) = i, ( 2/2,2/2)=2/2+ i 2/2, and . a) Draw a sketch of this triangle. b) What is the angle...
#3)Consider the asymptotic triangle with vertices(0, 1) = i, ( √2/2,√2/2)=√2/2+ i √2/2, and ∞.a) Draw a sketch of this triangle.b) What is the angle sum of this triangle. (Recall: the angle at ∞ has measure zero)c) Use the Gauss-Bonnet theorem to find the hyperbolic area of this triangle.d) Set up and compute a double integral that represents the hyperbolic area of this triangle.#4. Consider the hyperbolic segment connecting the points P = ( 3/2,1/2) and Q = ( 33/17 , 4/17).a) Find the midpoint of this segment. (Hint: Find an isometry that maps the line P←→Q to they-axis and takes P to (0, 1).b) Find the perpendicular bisector of this segment (i.e.describe where this semicircular archits the x-axis).c) Sketch the segment PQ and its perpendicular bisector.
