Determine the quadrant(s) in which (x, y) could be located

  • Thread starter nycmathguy
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  • #1
nycmathguy
Homework Statement:
Quadrants on the xy-plane.
Relevant Equations:
Linear Equations
Determine the quadrant(s)
in which (x, y) could be located.
Chapter 1, Section 1.1

13. x + y = 0, x ≠ 0, y ≠ 0

Let me see.

x + y = 0

I can solve for y.

y = - x

If y is - x, we get the point (x, - x).

This leads me to see a point in quadrant 4.

I can also solve for x.

If I do so, I get x = - y.

This leads to the point (-y , y), which takes me into quadrant 2.

I say the answer is quadrants 2 and 4.

You say?
 
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Answers and Replies

  • #2
3
3
(x, -x) doesn't necessarily have to be in quadrant 4. (Should x be positive?)
 
  • #3
PeroK
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Homework Statement:: Quadrants on the xy-plane.
Relevant Equations:: Linear Equations

Determine the quadrant(s)
in which (x, y) could be located.
Chapter 1, Section 1.1

13. x + y = 0, x ≠ 0, y ≠ 0

Let me see.

x + y = 0

I can solve for y.

y = - x
This is fine. Can you draw the graph of this function?
 
  • #4
nycmathguy
This is fine. Can you draw the graph of this function?
Are you asking me to draw y = x and y = -x on the same xy-plane?
 
  • #5
PeroK
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Are you asking me to draw y = x and y = -x on the same xy-plane?
Only ##y = -x##, which is the equation you have.
 
  • #6
35,129
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Homework Statement:: Quadrants on the xy-plane.
This is not a homework statement.
nycmathguy said:
Relevant Equations:: Linear Equations
Not an equation. If you can't think of any relevant equation, just leave it blank - don't just put something in for the sake of doing so.
nycmathguy said:
Determine the quadrant(s)
in which (x, y) could be located.
This is the homework or problem statement.
nycmathguy said:
Chapter 1, Section 1.1

13. x + y = 0, x ≠ 0, y ≠ 0

Let me see.
Please omit filler like "Let me see." You don't have to write down your every thought, only those that help us understand what you're doing. "Let me see" doesn't fall into this category.
nycmathguy said:
x + y = 0

I can solve for y.

y = - x

If y is - x, we get the point (x, - x).

This leads me to see a point in quadrant 4.
You're tacitly assuming that x is nonnegative, which is false for half of the possible numbers.
nycmathguy said:
I can also solve for x.

If I do so, I get x = - y.

This leads to the point (-y , y), which takes me into quadrant 2.
Same problem as above -- the point (-y, y) is in Quadrant II only if y >= 0.
nycmathguy said:
I say the answer is quadrants 2 and 4.

You say?
 
  • #7
nycmathguy
This is not a homework statement.
Not an equation. If you can't think of any relevant equation, just leave it blank - don't just put something in for the sake of doing so.
This is the homework or problem statement.
Please omit filler like "Let me see." You don't have to write down your every thought, only those that help us understand what you're doing. "Let me see" doesn't fall into this category.
You're tacitly assuming that x is nonnegative, which is false for half of the possible numbers.
Same problem as above -- the point (-y, y) is in Quadrant II only if y >= 0.

Can you provide an example of a HW Statement and Relevant Equations for those two categories? I have been corrected over and over and over again since joining this site.
 
  • #8
nycmathguy
This is not a homework statement.
Not an equation. If you can't think of any relevant equation, just leave it blank - don't just put something in for the sake of doing so.
This is the homework or problem statement.
Please omit filler like "Let me see." You don't have to write down your every thought, only those that help us understand what you're doing. "Let me see" doesn't fall into this category.
You're tacitly assuming that x is nonnegative, which is false for half of the possible numbers.
Same problem as above -- the point (-y, y) is in Quadrant II only if y >= 0.
Is my answer right or wrong?
 
  • #9
35,129
6,876
Can you provide an example of a HW Statement and Relevant Equations for those two categories?
For this thread:
Homework Statement::
Determine the quadrant(s)
in which (x, y) could be located for the line x + y = 0, x ≠ 0, y ≠ 0.

Relevant Equations::
None
Is my answer right or wrong?
Your answer is correct -- the line is in quadrants II and IV.

In another of your threads, about the diagonals of a parallelogram, these sections might look like this:
Homework Statement::
Prove that the diagonals of a parallelogram intersect at their midpoints.

Relevant Equations::
Midpoint of the line segment from (a, b) to (c, d): ##(x_m, y_m) = (\frac{a + c}2, \frac{b + d} 2)##
 
  • #10
PeroK
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Is my answer right or wrong?
Your answer is correct, but as @Quantour pointed out in post #2, your working was not right. And, you really took a long way round. When you have: $$y = -x$$ you should see that is the equation of a straight line through the origin. To graph a straight line you need only two points. We have the origin: ##x = 0, y = 0##. We might as well take ##x = 1## for our second point, which gives ##x=1, y = -1##.

That gives us a line through the second and fourth quadrants.
 
  • #11
nycmathguy
Your answer is correct, but as @Quantour pointed out in post #2, your working was not right. And, you really took a long way round. When you have: $$y = -x$$ you should see that is the equation of a straight line through the origin. To graph a straight line you need only two points. We have the origin: ##x = 0, y = 0##. We might as well take ##x = 1## for our second point, which gives ##x=1, y = -1##.

That gives us a line through the second and fourth quadrants.

At least I gave it a go, right?
 
  • #12
nycmathguy
This is not a homework statement.
Not an equation. If you can't think of any relevant equation, just leave it blank - don't just put something in for the sake of doing so.
This is the homework or problem statement.
Please omit filler like "Let me see." You don't have to write down your every thought, only those that help us understand what you're doing. "Let me see" doesn't fall into this category.
You're tacitly assuming that x is nonnegative, which is false for half of the possible numbers.
Same problem as above -- the point (-y, y) is in Quadrant II only if y >= 0.
Can you please provide an example of a Homework Statement and an example of Relevant Equations for those categories?
 
  • #13
35,129
6,876
Can you please provide an example of a Homework Statement and an example of Relevant Equations for those categories?
I already did this in post #9.
 
  • #14
nycmathguy
I already did this in post #9.

Tale the problem about find two missing numbers.

Here it is again:

Two numbers add up to 72. One number is twice the other. Find the numbers.

The HW Statement:
Find the numbers.

What would be the Relevant Equations in this case?
 
  • #15
35,129
6,876
Two numbers add up to 72. One number is twice the other. Find the numbers.

The HW Statement:
Find the numbers.
That's pretty vague. An improvement would be
Homework Statement::
Find two numbers whose sum is 72, with one number being twice the other.

What would be the Relevant Equations in this case?
You could leave that section empty.
 
  • #16
nycmathguy
You could leave that section empty.

This is what I'm talking about. Sometimes it is best to leave that section blank and for some questions it makes to complete the section.

What about for the following question?

I know how to solve the following equation. This is just an example.

Solve x + 5 = 10 for x.

Homework Statement:

Solve for x.

Relevant Equations:

Linear Equation

Is this right?
 
  • #17
35,129
6,876
I know how to solve the following equation. This is just an example.

Solve x + 5 = 10 for x.
The line above would be a good homework statement, but this problem is soooo simple it would hardly be worth posting a question about it.
 
  • #18
nycmathguy
The line above would be a good homework statement, but this problem is soooo simple it would hardly be worth posting a question about it.
Moving on....
 
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