GMAT prep coordinate geometry

awilhelm wrote:If ab does not equal 0 and points (-a, b) and (-b, a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?

1) xy > 0
2) ax > 0

how to approach?

Tough one. I believe the question stem tell us that a&b are either in 2nd or 4th quadrant.

1) xy > 0

XY is either in 1st or 3rd quadrant

(-x,y) can be in either 2nd or 4th

2) ax > 0

We dont know anything about X or a but other than they have the same sign!

INSUF

Together

We know that X is either - or +

SO X and A have the same sign

x = NEGATIVE
A = NEGATIVE

so Y = NEGATIVE
and B is NEGATIVE

and same applies for the opposite and all of the four numbers can be POSITIVE

So I changed my mind and go will be C! But I still need to hear a better explanation.

The stem tells us that a, b must be +,+ or -,- because of the signs of the coordinates. (-a, b) and (-b,a) will only be in the same quadrant is and b have the same sign. If a is neg and b is pos, then the first point will be in pos,pos quadrant and the second point will be in neg,pos quadrant, so not the same (as is true for the inverse). If both x,y are pos, they are in the neg,pos quadrant and if both are neg, they are in the pos,neg quadrant.

1) xy>0 tells us that x,y must be +,+ or -,-, which is all we know about ab also. So, -x,y could be in the same quad as (-a,b) or it could be in the opposing one. Not Suff

2) ax >0 Not sufficient on its own as we know nothing about y from this statement.

However, when combined, we know that x,y must be +,+ or -,- from statement 1 and statement 2 ties together x,y and a,b so that if a is + then x must be + (and if a is neg, then x must be -) so if a,b is +,+, then x,y must be +,+ (same for -,-)

Therefore C.

-Carrie