Suppose \gamma is any curve in the upper half-plane (the hyperbolic plane where y>0) connecting (x,y) and (x',y'). Prove that the hyperbolic length of \gamma is at least |\ln (y',y)|.

I know that if x = x', then the geodesic that connects the two is simply the Euclidean line segment between the two points, and if x\ne x', then the geodesic connecting the two points are arcs of Euclidean semicircles centered on the x-axis. Other than that, I really don't know where to begin. Thanks.