Hmm... tricky question. Formally it must use a preposition, but in everyday use we omit it for this verb. So, if this duo's question is a formal question, we will read the a as a preposition and there will be no article (it's facultative, and formal register tends to omit it more often). But it can be viewed as an informal question also, then the a will be an article. Il try to summarize it:
Ele responde (a) minha carta: informal. It has no preposition and the article is facultative
Ele responde a/à minha carta: formal. It has preposition and the article is facultative
It is preposition. See here - http://dictionary.reverso.net/portuguese-english/responder
If we use the English sister word, respond then it becomes in the translation, He responds to my letter so I would peg it ("a") as a preposition in Brazilian forms, and that in Euro PT it should be, Ele responde à minha carta (with the contraction of the preposition + article which is less optional outside of Brazil).
Great question (made me think, and I like that)! :)
Could "á minha carta" work? I was combining the preposition "a" with the article "a".
I agree. But weirdly duolingo warns me against writing this (and warns against using "o meu...", "a minha...", etc. in general)
The preposition is necessary here in the English (as with the Portuguese) when using "respond" but not with "answer".
- He responds to my letter
- He answers my letter
As to the differences between the two in regards to meaning, there is little here but, in other circumstances, responding does not always mean answer. For instance: "I have a question" "Okay, what is your question?" For this the response was a question and not an answer.