Problem Solving

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

Source: Manhattan Prep

BTGmoderatorDC wrote: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)

Source: Manhattan Prep

Just a quick observation that is (I hope) interesting in its own right:

If x*y and w*z are both different from zero, points (x,y) and (w,z) will be in the same quadrant if, and only if,
x*w> 0 ("x-coordinates" have the same sign) and y*z>0 ("y-coordinates" have the same sign).

Conclusion:

(B) is refuted, because a and -a (x-coordinates in question stem and in this alternative choice) do not have the same signs (a is not zero)
(C) is refuted, because if a and b (x-coordinates...) have the same signs , then b and -a (y-coordinates...) don´t have
(D) is refuted, because b and -b (y-coordinates...) do not have the same signs (b is not zero)
(E) is refuted, because if a and -b (x-coordinates...) have the same signs , then b and a (y-coordinates...) don´t have

Regards,
fskilnik.