The correct answer is A. He asked me, “Why are you late?”
In this sentence, the speaker is asking the listener why they are late. The speaker is using the second person pronoun “you” to address the listener, and the verb “are” to indicate that the listener is currently late. The speaker is also using the interrogative pronoun “why” to ask a question.
The other options are incorrect because they do not accurately reflect the meaning of the sentence. Option B, “He asked me, ‘Why I was late,'” is incorrect because the speaker is not asking about the listener’s past tense. Option C, “He asked me, ‘Why you are late,'” is incorrect because the speaker is not addressing the listener as “you.” Option D, “He asked me, ‘Why am I late,'” is incorrect because the speaker is not asking about their own lateness.