This question deals with the upper half plane model of hyperbolic geometry. Points are
represented by complex numbers with positive imaginary component.
Let P = −2 + 7i,Q = 3 + 2i and R = 3 + 8i be points in the hyperbolic plane.

(i) Determine the unique hyperbolic lines joining the pair of points Q and R and the
pair P and Q.

(ii) Calculate the hyperbolic distances: h(Q, R) between Q and R, and h(P,Q), between
P and Q.

Question

This question deals with the upper half plane model of hyperbolic geometry. Points are
represented by complex numbers with positive imaginary component. 
Let P = −2 + 7i,Q = 3 + 2i and R = 3 + 8i be points in the hyperbolic plane.

(i) Determine the unique hyperbolic lines joining the pair of points Q and R and the
pair P and Q.

(ii) Calculate the hyperbolic distances: h(Q, R) between Q and R, and h(P,Q), between
P and Q.