Final answer:
The correct preposition to fill in the blank in the dialogue is 'à la'. It is used before feminine singular nouns like 'bibliothèque' and means 'to the' in English.
Step-by-step explanation:
The correct preposition to fill in the blank in the dialogue is à la.
So the complete sentence would be: Tu vas à la bibliothèque? which translates to 'Are you going to the library?'
This preposition is used before feminine singular nouns like 'bibliothèque' and means 'to the' in English.
Learn more about Prepositions in French