。
Yumi goes to the park to play tennis.
Literal
Yumi [topic-は] tennis [object-を] do-[purpose-に] park [to-へ] go-[polite-ます].
テニスをしに — the purpose-に attached to the verb stem し (from する). This is the ~に行く pattern with a specific activity (playing tennis). Literally 'goes to the park for [the doing of] tennis.' Common Japanese purpose-of-going structure.