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Math Help - Which Quadrant?

  1. #1
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    Which Quadrant?

    In which quadrant is P(x,y) located if xy < 0 and x + y < 0?

    MY WORK:

    For xy > 0, I figured that for this to be true, both x and y must be positive values.

    In other words, x and y cannot be 0 and negative.

    For x + y < 0, one of the variables must be bigger than the other and negative.

    I don't know where to go with this question in order to find the quadrant.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by sharkman View Post
    In which quadrant is P(x,y) located if xy < 0 and x + y < 0?

    MY WORK:

    For xy > 0, I figured that for this to be true, both x and y must be positive values.

    In other words, x and y cannot be 0 and negative.

    For x + y < 0, one of the variables must be bigger than the other and negative.

    I don't know where to go with this question in order to find the quadrant.
    Given a>0,b>0, What if x=-a and y=-b? Then xy=(-a)(-b)=ab>0. So x and y can also be negative! (this now tells us P(x,y) is either in the first or third quadrant)

    Then it follows that x+y=(-a)+(-b)=-a-b<0. This satisfies the conditions of P\!\left(x,y\right) falling into the third quadrant.

    Does this make sense?
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  3. #3
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    yes...

    Quote Originally Posted by Chris L T521 View Post
    Given a>0,b>0, What if x=-a and y=-b? Then xy=(-a)(-b)=ab>0. So x and y can also be negative! (this now tells us P(x,y) is either in the first or third quadrant)

    Then it follows that x+y=(-a)+(-b)=-a-b<0. This satisfies the conditions of P\!\left(x,y\right) falling into the third quadrant.

    Does this make sense?
    Very easily explained.
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