In this paper, we study the geometry of trisections of certain rational elliptic surfaces. We utilize Mumford representations of semi-reduced divisors in our study and demonstrate its effectiveness in dealing with equations of trisections and related plane curves. As an application, we construct plane curves with interesting properties. Especially, we give explicit equations of plane curves which give a family of Zariski pairs consisting of cubic-conic-line arrangements that degenerate to the same conic-line arrangement.
