"Is it yours?"
Translation:Er det din?
Not in this sentence, I guess.
Here the "det" addresses "er" while the pronoun "din" is referred to an object that we don't know. Each of them (det and din) has his own gender. They are not correlated.
So if we would have "hus" as object, the sentence would be: "Er det dit hus?"
If we have"tallerken" as object, it would be: "Er det din tallerken"
This is a guess, but someone with better knowledge than me can confirm!
One needs to pay close attention to this sentence (as with all unspecific sentences). 'Is it yours?' - the 'it' can be yours (dit/din) - the it referring to neutral or common nouns ( the type of it ): Er det din/Er det dit, and it can also be you guys's (Er det jeres). I think the confusion is coming from trying to have 'it' decline according to its gender, when the sentence is changing according to the person possessing it. The 'it' isn't doing any possessing. I am also guessing that Danish has some sort of preference for the neuter gender (like most languages masculine) that 'det' is preferred in the abstract for it, rather than use din.