Did you come to get me with 〜のだ

Grammar Explanation

ふらいんぐうぃっち » Volume 1 » Page 7

After getting off the intercity bus, Makoto is greeted by her cousin Kei.

“Did you come to get me?”
Literal: “Is it that you came to get me?”
「あぁ そうだよ」
“Yeah, that’s right.”

Makoto’s incomplete observation is that her cousin is at the bus stop. The part she is unaware of is why he is there. She comes up with the most obvious reason, that Kei came to the bus stop to get her and show her to his house where she will be staying.

There was never an exchange where Makoto asks why Kei is there. Asking if it’s the case that he’s picking her up implies that she’s inquiring as to the reason why he’s there.