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Determine the Quadrants

 
 
nycdad
 
Reply Sun 16 May, 2021 07:09 pm
Determine the quadrant(s)
in which (x, y) could be located.

1. x + y = 0, x ≠ 0, y ≠ 0

2. xy > 0

I'm not too sure about question 1. Any hints?

For question 2, x times y > 0.
This happens in quadrant 1.
However, if x and y are both negative, then xy > 0.
I know that x and y are both negative in quadrant 3.
I think the answer for question 2 is quadrants 1 and 3.
Is this right?
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maxdancona
 
  2  
Reply Sun 16 May, 2021 08:16 pm
@nycdad,
Yes, your logic for question #2 is correct.

For question #1 try the following points.

(1,1)
(1,-1)
(-1, -1)
(-1, 1)
nycdad
 
  1  
Reply Sun 16 May, 2021 09:40 pm
@maxdancona,
Are you saying the answer for question 1 is all 4 quadrants?
maxdancona
 
  1  
Reply Mon 17 May, 2021 03:22 am
@nycdad,
No, I am not saying it is all 4 quadrants.

Take the first point I suggest... (1,1). Does that meet the condition x + y = 0? Is there any point in quadrant 1 that meets that condition?
nycdad
 
  1  
Reply Mon 17 May, 2021 06:15 pm
@maxdancona,
For question #1 try the following points.

(1,1)
(1,-1)
(-1, -1)
(-1, 1)

x + y = 0

Plugging in the point (1,1), I get 1 + 1 = 0, which is a false statement.

Plugging in the point (1, -1), I get 1 - 1 = 0, which is a true statement.

Plugging in the point (-1, -1), I get -1 - 1 = 0, which is a false statement.

Plugging in the point (-1, 1), I get - 1 + 1 = 0, which is a true statement.

Answer: For x + y = 0, points in the form (x, y) are located in quadrants 2 and 4.
maxdancona
 
  2  
Reply Mon 17 May, 2021 07:33 pm
@nycdad,
Yes, that's correct.

You should confirm a few more points in each quadrant and you certainly should find a few more points that match the equalities in the second and fourth quadrant.

But yes! I think you have it.
nycdad
 
  1  
Reply Mon 17 May, 2021 08:25 pm
@maxdancona,
Thanks. I love math. I graduated from college in 1994 but recently decided to revisit precalculus. Are you willing to take this journey with me? I need someone to help me as I go through the textbook. I am not a student. However, I have several college degrees in areas other than mathematics. You say?
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