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.)                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                      
  III , y/r

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. We have the ratio Y divided by R and we have two answer choice options, answer choice, a positive or answer B negative. So to identify if our ratio is positive or negative, we first need to look at the signs of Y and R in relation to the location of our point. So we can begin with the sign of R. And so to determine the sign, we just need to look at the expression for R where we can see that both X and Y are squared. So that tells us that no matter what X value or Y value we have in our expression, we will always return a positive value. Therefore, we know that R is always going to be positive. And now looking at the sign of why we need to look back at our problem statement where we see we are in the fourth quadrant. So we want to draw out our Cartesian plane. So we first have a vertical line to represent the Y axis and then a horizontal line for the X axis. And we are in the fourth quadrant. So we just need to recall that this quadrant is the bottom, right square on our plane. So in the bottom right square, we have our point XY and this is also the fourth quadrant. And now we just want to notice that along the X axis, we have positive values. So we are along the positive X axis. But more importantly, we need the sign of Y. And here we can notice that in the fourth quadrant, we are along the negative Y axis. And so this tells us that why is always going to be negative in our ratio. And so now looking back at our ratio, we have A Y is negative and R is positive. So we have a negative divided by a positive and this returns us a negative ratio. And therefore we are left with answer choice B where again our ratio is always going to be 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.) III , y/r

Key Concepts

Quadrants of the Cartesian Plane

Trigonometric Ratios

Radius in Polar Coordinates

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