Concept Check Suppose that the point (x, y) is in the indicated q...

Question

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that  r = √(x² + y²) .(Hint: Drawing a sketch may help.)                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                      
  IV , x/y

Accepted Answer

Hey, everyone here we are asked if the point Xy is in the third quadrant identify if the given ratio is positive or negative. Here, we have the ratio X divided by Y. We have two answer choice options, answer choice, a positive or answer B negative. So to begin identifying if our ratio is positive or negative, we first want to look at the location of our point on the xy plane. So drawing our plane, we have a vertical line to represent the Y axis as well as a horizontal line to represent the X axis. And now in the problem statement, it states we are in the third quadrant that our point is in the third quadrant. So we just want to recall that on a Cartesian plane, the third quadrant is the bottom left square here. And so again, we are in the bottom left square and we have our point Xy and this is the third quadrant. And so now we just want to notice that we are along the negative X axis as well as the negative Y axis. So now looking back at our ratio again, we have X divided by Y. So we know X is always going to be negative since we are in the third quadrant. And Y for the same reason is also always negative. So we have a negative divided by a negative and this just gives us a positive ratio. Therefore, we are left with answer choice A where again, our ratio is positive. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) IV , x/y