Hello everyone, this is probably simple, butI don\'t understand and could use an

Question

Hello everyone, this is probably simple, butI don't understand and could use any help. Thank you.

Question: In whichquadrant(s) could a point be located if its coordinates arereciprocals of each other?

I did not understand so I sentthis to my teacher:

I believe the answer is: the same quadrant as the originatingcoordinates. for example: If (3,5) or 3(x),5(y) = 3/5 then wouldthe reciprocal plot be (5,3)?

or would the reciprocal for (3,5) be (1/3,1/5)? If the answer isthe secondary then wouldn't graphing this get you 2 points graphedfor the ordered pair ( one for 1/3 and one for 1/5) instead of 1,since I believe when graphing fractions x is the numerator and y isthe denominator (or would there be a way to simplify)?

The response to my question from my teacher was:
where would the coordinates be (x,1/x) or (1/y,y)?

That could happen in two places. (3,1/3) and (-3,-1/3) areexamples.



I am completely clueless if he answered my question and or what heis asking me. Thank you for your help ahead of time.

Explanation / Answer

So, for example, if x=2, then (2,1/2) is a possible coordinatepair.
It seems to me that your intuition for this problem iscorrect, in that the coordinates would have to be in a quadrantwhere their signs are the same.
When you take the reciprocal of 2, you don't change it's sign. Therefore, the example of (2,1/2) must be in QuadrantI.
This is NOT the only quadrant that the coordinates could bein. They could also be in Quadrant III, because if you havex=-2, then you have (-2,-1/2).

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