If (-x, y) is in the same quadrant as (-a, b), then x and a have the same sign, and y and b have the same sign.

You're certainly right that a and b have the same sign; that information is in the question itself. I wonder if you combined both statements accidentally when you chose your answer.

Statement 1 alone tells us that x and y have the same sign; that isn't enough unless we know some relationship between the signs of x and y and the signs of a and b.

Statement 2 alone tells us that a and x have the same sign. We still don't know about b and y.

Together, from 1, y and x have the same sign, and from 2, x and a have the same sign, and from the question, a and b have the same sign. So every letter has the same sign, and we can certainly answer the question.