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A: Why does the article type (definite /indefinite) change the preposition before the word 'hotel' ?
I don't understand why you find it strange, correct me if I'm wrong but you have the same usage in English.
Q: "Where did you sleep last night, you were not home?"
A: "I slept at the hotel" --> "J'ai dormi à l'hôtel"
Q: "You like your trip? Tired of sleeping in your car?"
A: "Yes, but last nigh...