Adjectives also receive the definite article when the noun they modify is definite. In this case, "baytii" isn't preceeded by the definite article, so can you figure out why we still need the al- before jadiid? It's because "baytii," "my house," is still a definite construct in that it refers to a specific house. Proper nouns, question words, pronouns, and nouns possessed by a definite noun are all considered definite in Arabic. Also nouns described by relative clauses, since you can only use a relative clause to describe a definite noun in Arabic: "the house that I bought," البيت الذي اشتريته, is valid Arabic, "a house that I bought," *بيت الذي اشتريته, isn't. It's a very common mistake that Western learners of Arabic make in my experience.