  We present a unified description of birational representation of Weyl groups
associated with T-shaped Dynkin diagrams, by using a particular configuration
of points in the projective plane. A geometric formulation of tau-functions is
given in terms of defining polynomials of certain curves. If the Dynkin diagram
is of affine type ($E_6^{(1)}$, $E_7^{(1)}$ or $E_8^{(1)}$), our representation
gives rise to the difference Painlev\'e equations.
