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Comment on Which Quadrant?
What about x= -2 and y=-3?
Are you trying to show that
Are you trying to show that the combined statements are not sufficient? If so, I should point out that x= -2 and y= -3 does not meet the condition in statement 1 (xy < 0), because (-2)(-3) = 6, and 6 is not less than zero.
I think he's suggesting
Ahh, good point
Ahh, good point/interpretation!
So, statement 2 is not sufficient because the point could lie in THREE possible quadrants.
Hi Brent,
In statement 2, X-Y>0, if we picked up a negative number for Y, would not the inequality X-(-Y), which would result in a positive number to rely on quadrant 1? Thank you!
Not quite.
Not quite.
If y is negative, then there are many possible cases that satisfy the inequality x - y > 0:
CASE A) x = 3 and y = -1. In this case, (x,y) is in quadrant IV.
CASE B) x = -1 and y = -3. In this case, (x,y) is in quadrant III.
Also note that there's nothing in statement 1 to suggest that y is negative. So, we must also consider positive values for y such as:
CASE C) x = 3 and y = 1. In this case, (x,y) is in quadrant I.
Does that help?
Cheers,
Brent
It does, thank you Brent for
Hi Brent. Would statement 2
You're correct to say that,
You're correct to say that, in Quadrant IV, x-y is always positive.
So, the point COULD be in Quadrant IV.
However, there are points in other quadrants where x-y is also positive.
For example, the point (3,2) lies in Quadrant I, and here x - y = 3 - 2 = 1, which is positive.
So, the point COULD be in Quadrant I.
Likewise, the point (-1,-5) lies in Quadrant III, and here x - y = (-1) - (-5) = 4, which is positive.
So, the point COULD be in Quadrant III.
Since we can't be certain which quadrant the point lies, statement 2 is not sufficient.
Does that help?
Cheers,
Brent