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.)                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                      
  I , r/y

Accepted Answer

Hey, everyone here we are asked if the point Xy is in the fourth quadrant identify if the given ratio is positive or negative. And we need to note that R is equal to the square root of X squared plus Y squared. And we are given the ratio R divided by Y. Here we have two answer choice options, answer choice, a positive or answer B negative. So we want to begin here by taking a look at our expression given for R. And here we see that both the X and Y terms are squared. So this tells us that R is always going to be positive because again, both possible values are squared which will always a return a positive value. And now looking at our sign for Y, we look back at our problem statement where we are told that our point Xy is in the fourth quadrant. So quickly drawing out our Cartesian coordinate system, we have a vertical line for the Y axis and a horizontal line for the X axis. And again, we are in the fourth quadrant which is the bottom right of our graph. So we are in the fourth quadrant and we can notice here that we are in the positive X axis, however, we are in the negative Y axis. So here we know that Y is going to be negative. And so looking back at our ratio, we see we have a positive divided by a negative. So this tells us that our ratio will just be negative. So here we are left with answer choice B where again our given ratio is negative. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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.) I , r/y

Key Concepts

Quadrants of the Cartesian Plane

Trigonometric Ratios

Distance Formula and r

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