Curt means using so few words that it comes across as rude. The answer that is technically polite and clearly not.
It describes replies, nods and manner, and a curt reply is one that closes the conversation. What makes it curt is the gap between the brevity and what the situation expected, since the same words in a hurry would be fine. The adverb curtly is common in dialogue tags. Brusque is its close neighbour and means the same discourtesy delivered a little more forcefully.
1adjectivecurtNoticeably brief to the point of rudeness.
“He gave a curt nod and walked on.”
Proto-Indo-European
*(s)ker-
Latin
curtus — shortened
English, today
curt
From the Latin curtus (“shortened”). Cognate with Dutch kort, German kurz, Galician curto, French court, Italian corto, Portuguese curto, and Spanish corto. a doublet of short.
Etymology from Wiktionary, CC BY-SA