"The boy paints the large tree."
Translation:A fiú festi a nagy fát.
It is because of the difference between "a/az" (the) and "egy" (a/an)
For exemple: A fiú fest EGY fát. - The boy paints A tree. A fiú festi A fát. - The boy paints THE tree.
Is the rule that one always adds an "i" at the end of the verb when the object is preceded by a definite article such as "the" (a or az in Hungarian) ?
Yes, if the subject is third person singular: http://www.verbix.com/webverbix/go.php?D1=121&T1=fest Not sure if that is always the case, though (still learning, as well) ¯_(ツ)_/¯
Not always, it depends on the vowel harmony. It can also be -ja: adja, rajzolja, mondja.