"That is my girl."
Translation:Det er jenta mi.
'den/det' is used when you're referring to something you've already talked about. When you're introducing something new, you'd use 'det'. 'det/den' is in that case replacing a noun, while 'det' is just something unspecified.
"Det er katten min. Den har blå øyne." instead of "Det er katten min. Katten min har blå øyne".
In both English and Norwegian, people are more likely to say, "Do you see that girl? She is mine." Even if the speaker doesn't mind the redundancy of repeating "my girl/jenta mi," the second sentence would start with, "she/hun." Make sense?
On the other hand, if you were to replace "my girl" with "my cabin," yes, you'd still say, "Det er hytta mi."
Here's a flowchart that might help:
As someone kindly explained at another question, you need to use "mi" after a word that ends in "a", like "jenta mi", or "hytta mi", or "boka mi", or "bygda mi". For a more logical solution, you could always use min instead of mi, by choosing not to use "a" as a termination, and just use "en". It is grammatically correct to use "jenten min" for example. I used "Det er jenten min" and it was correct. However, i believe that in spoken language, it is more preferable to use "jenta" than "jenten".
It is a question of dialect and of register - in some places, like in Bergen and parts of the Oslo area, people say "jenten" exclusively. Most Norwegians will say "jenta". Many will tend to use the masculine (-en) ending when speaking or writing in a high register, but they may still use the feminine (-a) ending with words designating an actual female person, like "jenta". In more casual speech, people will ALWAYS say "jenta" if they have this form in their dialect at all. So I would recommend learners to use "jenta" rather than "jenten", at least in speech.
The possessive, mi, is used only with feminine nouns. You'll need min with masculine nouns, such as gutt/gutten and mann/mannen.
Just as "my girl" in English could imply "my daughter" or "my girlfriend," jenta mi could potentially mean either of those.
In English, "my boy" can mean "my son," but isn't used to mean "my boyfriend." It's the same in Norwegian.
"My wife" is "kona mi" (more common than the masculine declension, konen min). Kvinnen min/Kvinna mi can be used for "my woman," or "my lady friend," which isn't necessarily my wedded wife.
"Mannen min" can mean both "my husband," or "my man."
The choice of possessive has to agree with the gender of the noun that's being possessed.
Use mitt, ditt, sitt with neuter nouns, e.g., huset mitt - my house.
Use mi, di, si with feminine nouns, e.g., hytta mi - my cabin.
Min, din, sin with masculine nouns, e.g., bilen min - my car
And, optionally, with feminine nouns, e.g., boka mi or boken min - my book.