have or havn't: Haven't you been to New York? - No, I haven't / No, I have

[Huda2]

as we know if the question is negative the answer is positive. so, why the third choise is best?
"Haven't you been to New York?"
"_____ been there."
Yes, I haven't
Yes, I wasn't
x No, I haven't
No, I have

[Milanya]

The answers with Yes and No can be either complete sentences : Yes, I am; Yes, I did; Yes, I have; or No, I am not; No, I did not; No, I have not.
or "abbreviated forms" : Yes. No.
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con·text - The part of a text or statement that surrounds a particular word or passage and determines its meaning.

[Huda2]

sorry, I didn't understand what are you meaning?