Right Answer: Yo voy a la biblioteca
(I go to the library)
This sentence is written with the verb ir (to go) in present indicative with the 1st person in singular yo (I) as:
yo voy (I go)
In addition biblioteca (library) is a singular feminine noun; therefore the correct defined article to use is la (the):
la biblioteca (the library)
The other options are incorrect because the sentences are not written according the rules explained above.
