The SL_2(R) action on a hyperbolic plane is a basic example of the group action. In this talk, we will briefly review the geometry of hyperbolic plane as the homogeneous space SL_2(R) over SO(2). If there is more time left, we will construct a tree where SL_2(Q_p) acts and talk about similarities and differences between two actions. Here Q_p is the completion field of the rational field with respect to p-adic norm.