1. I met him at the corner.

2. I met a beggar at the corner.
3. I met the beggar at the corner.
------------------------------
What is the part of speech of 'at the corner'? Is it an adjective phrase or an adverbial phrase? Or can it be both?
My explanation for #2 is as follows.

Where did you meet a beggar? I met a beggar at the corner. If this is the answer to the question, 'at the corner' is an adverbial phrase.

Which person did you meet? I met a beggar at the corner. I met a beggar who was at the corner. In both answers, 'at the corner' is an adjective.

What do you think about my explanation?

This is correct:

What is the part of speech of 'at the corner'? Is it an adjective phrase or an adverbial phrase? Or can it be both?
My explanation for #2 is as follows.

Where did you meet a beggar? I met a beggar at the corner. If this is the answer to the question, 'at the corner' is an adverbial phrase.


However, in neither sentence would "at the corner" be considered an adjective. It's telling where, and that applies to adverbs.
http://www.chompchomp.com/terms/adverb.htm

OK, I thought of a way to phrase that so "at the corner" would act as an adjective!!

The man at the corner is my brother.
(Adjectives need to be as close to the noun they're modifying as possible.)

Your explanation is generally correct. "At the corner" can have different functions depending on the context, and it can be both an adverbial phrase and an adjective phrase.

In the first sentence, "at the corner" functions as an adverbial phrase because it answers the question "Where did you meet him?" It provides information about the location of the meeting.

In the second sentence, "at the corner" modifies the noun "beggar" and answers the question "Which person did you meet?" It describes the specific beggar that was at the corner, so in this case, it functions as an adjective phrase.

In the third sentence, "at the corner" functions as both an adverbial phrase and an adjective phrase. It provides information about the location of the meeting like in the first sentence, but it also describes the specific beggar that was at the corner.

Overall, it's important to consider the context to determine how "at the corner" is functioning in a sentence. It can vary between being an adverbial phrase or an adjective phrase depending on the specific sentence and the question it is answering.