"Did you see my new sweater?"

Translation: Ти бачила мій новий светр?

[GeneM.]

I know the past tense ending is determined by gender, but in a sentence like this who determines the gender: the person asking the question or the person being asked the question?

[deactivated user]

«Ба́чила» refers to «ти», to the person doing the 'seeing', that is, to the person who is being asked the question.

[sagitta145]

The subject of the sentence.