Coordinate Geometry

[awilhelm]

If ab is not equal to 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

[krisraam]

Answer is E.

Both together are not sufficient.

(-a,b) and (-b,a) are in the same quadrant when a and b are both positive or negative. So they can be either 2nd or 4th quadrant.

xy > 0 ==> either x and y are both positive or both negative.

if positive it will be in 2nd Quadrant if negative it will be in 4th Quadrant. Not sufficient.

ax>0 ==> if a is positive x has to be positive. if a is negative x has to be negative. Not sufficient.

Both together

If a is positive x has to be positive, y has to be positive . 2nd Quadrant
if a is negative x has to be negative, y has to be negative 4th quadrant

Answer is E

Thanks
Raama

[ajmoney09]

I say the answer is C....

Statement one says XY>0

Which means both ar epositive or both are negative

Statement 2 says AX > 0

Which means X is positive or negative pending what X is equal to.

Now lets go back to the stem....

given the information if both a and are positive then (-a,b) and (-b,a) are in Q2....if both are negative then they are both in Q4

Now lets go back to statement 2....If A is negative then X is negative....and then adding that information to statement one we know Y is also negative....telling us which Quadrant (-X,Y) is located in...which will be in the SAME quadrant as (-a,b) and (-b,a)

Now if A is positive then both (-a,b) and (-b,a) are in Quadrant 2....if A is positive then X is positive meaning Y is positive which means (-x,y) is in the same Quadrant as (-a,b) and (-b,a).....Sooo this is my reasoning behind the C...

Whats the OA?

[awilhelm]

OA is E.

[ajmoney09]

Answer is E.

Both together are not sufficient.

(-a,b) and (-b,a) are in the same quadrant when a and b are both positive or negative. So they can be either 2nd or 4th quadrant.

xy > 0 ==> either x and y are both positive or both negative.

if positive it will be in 2nd Quadrant if negative it will be in 4th Quadrant. Not sufficient.

ax>0 ==> if a is positive x has to be positive. if a is negative x has to be negative. Not sufficient.

Both together

If a is positive x has to be positive, y has to be positive . 2nd Quadrant
if a is negative x has to be negative, y has to be negative 4th quadrant

Answer is E

Thanks
Raama

You got the same thing I got, but it is asking if the point is in the same Quadrant as a and b....and if you make A positive then it is in 2nd Quadrant, not just point (-x,y) but also (-a,b) and (-b,a) are in 2nd Q.

same goes for if a is Negative....its in the 4th Q, but all three points are in the same Quadrant. which is Q 4

[krisraam]

yeah you are right. It should be C.

I misunderstood the question. I was trying to prove that we can't say which quadrant the point is in..


Thanks
Raama