Problem Solving

Hello,

I had a question here:

Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A) (-b, -a)

B) (-a, -b)

C) (b, -a)

D) (a, -b)

E) (-b, a)

OA: A


I picked a = 2, b = 3 and then got the following values for the answer choices:

(-b, -a ) = (-3, -2)
(-a, -b ) = (-2, -3)
(b, -a ) = (3, -2)
(a, -b ) = (2, -3)
(-b, a ) = (-3, 2)

I am thinking that for the correct answer, one of the above choices should lie in the same quadrant as a = 2 and b = 3 i.e. Quadrant 1. None of the above choices meet that condition.

I then picked a = -2 and b = 3 and they lie in the Quadrant 2. Now we have:

(-b, -a) = (-3, 2)
(-a, -b) = (2, -3)
(b, -a) = (3, 2)
(a, -b) = (-2, -3)
(-b, a) = (-3, -2)

In the above choices, (-b, -a) = (-3, 2) also lies in Quadrant 2. Hence, this would be a correct value. I was wondering if there is a way we can directly test the answer choices for a point in Quadrant 2 without testing the answer choices for a point in Quadrant 1? Thanks a lot for your help.

Best Regards,
Sri