"The kitchen is yours."
Translation:La cucina è tua.
I don't think so, no.
"La cucina è tua" would mean "The kitchen is yours (and not mine)."
The kitchen is YOURS. Not his, not hers.
"La cucina è la tua" would mean "The kitchen (as opposed to something else) is yours."
The KITCHEN is yours. Not the back office, not the utility closet, not the kitchen in my house.
No, "sono" is the wrong conjugation.
I am = io sono
you (s) are = tu sei
he/she/it is = lui/lei è
we are = noi siamo
you (pl) are = voi siete
they are = loro sono
So it's either:
La cucina è (la) tua
La cucina è (la) vostra
Le cucine sono (le) tue
Le cucine sono (le) vostre
depending on how many kitchens and how many people you're talking to.
The first thing to understand is that these all must agree with what is possessed and never with who possesses it.
la tua = your singular, feminine thing
le tue = your plural, feminine things
il tuo = your singular, masculine thing
i tuoi = your plural, masculine things
These are only used with the singular pronoun "tu". For the plural pronoun "voi", it would be:
la vostra = your singular, feminine thing
le vostre = your plural, feminine things
il vostro = your singular, masculine thing
i vostri = your plural, masculine things