A quadrant is a certain configuration of x and y on the positive/negative line.
For example, all of the points in the first quadrant will have a positive x coordinate and a negative y coordinate.
All of the points in the second quadrant will have a negative x and a positive y.
III: negative x, negative y.
IV: Positive x, negative y.
so if the points are in the same quadrant, it means that the x and y coordinates of the two points have the same sign between them. We don't know which quadrant, but we know that
-a and -b are positive or negative together: either both positive or both negative. the same goes for the y coordinates, but it's the same message: a and b have the same sign.
when asking if the point -x,y is in the same quadrant, the question is asking whether -x has the same sign of -a and -b, and whether y has the same sign as a and b: basically, do x and y share the same sign as a and b.
Stat. (1) tells you that x and y share the same sign: either both positive, or both negative.
IS, since you don't know anything about a and b.
Stat. (2) tells you that a and x share the same sign: either both positive or both negative. ALONE, this is insufficient, since we don;t know anything about y; But
combined, we know that a has the same sign as x (stat. (2)), and x in turn has the same sign as y (stat. (1)), so it follows that x and y have the same sign as a (and b, from the question stem). So regardless of which quadrant it is, we know that the point x and y will have the same carachteristics as the other two points, and the answer is a definite "yes". Sufficient.
