Questions & Answers about Эта книга принадлежит другу.
Because книга is a feminine singular noun, and the demonstrative this has to agree with it.
- masculine: этот
- feminine: эта
- neuter: это
So:
- эта книга = this book
If the noun were masculine, you would use этот, for example этот стол (this table).
Because the verb принадлежать (to belong) requires the dative case for the person or thing that something belongs to.
So in this sentence:
- книга is the thing doing the grammatical action
- другу is the person to whom the book belongs
That is why друг changes to другу.
A useful pattern is:
- X принадлежит Y = X belongs to Y
where Y is usually in the dative.