Determine Quadrants For (x, y)

[nycmathdad]

Exercises 9–14, determine the quadrant(s)
in which (x, y) could be located.

9. x > 0 and y < 0

I say this is quadrant 4.

10. x < 0 and y < 0

I say this is quadrant 3.

11. x = −4 and y > 0

I say this is quadrant 2.


12. x < 0 and y = 7

I say this is quadrant 2.

13. x + y = 0, x ≠ 0, y ≠ 0

Not sure about 13.

14. xy > 0

I say this is quadrant 1.

You say?

 

[JeffM]

13 is sort of a trick question because it depends on interpreting words.

If x and y are in quadrant 3, then both values are negative and so their sum must be negative..

If x and y are in quadrant 1, then both values are positive and so their sum must be positive.

Now what is the situation in the remaining two quafrants and what do the words of the question mean?

In 14, you know better. What is -3 * (-2)?

 

[nycmathdad]

13 is sort of a trick question because it depends on interpreting words.

If x and y are in quadrant 3, then both values are negative and so their sum must be negative..

If x and y are in quadrant 1, then both values are positive and so their sum must be positive.

Now what is the situation in the remaining two quafrants and what do the words of the question mean?

In 14, you know better. What is -3 * (-2)?

quadrants do these refer to?

The line y = -x passes through the origin from quadrant 2 down to quadrant 4. It's the opposite line to y = x.

For question 14, if x > 0 and y > 0, this is quadrant 1. If x < 0 and y < 0, we are in quadrant 3.

 

[JeffM]

The line y = -x passes through the origin from quadrant 2 down to quadrant 4. It's the opposite line to y = x.

For question 14, if x > 0 and y > 0, this is quadrant 1. If x < 0 and y < 0, we are in quadrant 3.

Yes, you have it for 14.

With respect to 13, I think you have it.

If the points are in quadrant 1, the sum of the coordinates WILL be positive.

If the points are in quadrant 2 or 4, the sum of the coordinates MAY be positive.

If the points are in quadrant 3, the sum of the coordinates WILL NOT be positive.

The problem revolves too much about the differences in meaning of the modals “will,” “may,” and “can” for my taste.

 

[nycmathdad]

Yes, you have it for 14.

With respect to 13, I think you have it.

If the points are in quadrant 1, the sum of the coordinates WILL be positive.

If the points are in quadrant 2 or 4, the sum of the coordinates MAY be positive.

If the points are in quadrant 3, the sum of the coordinates WILL NOT be positive.

The problem revolves too much about the differences in meaning of the modals “will,” “may,” and “can” for my taste.

Cool.