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 , r/y

Accepted Answer

Hey, everyone here we are asked if the point Xy is in the second 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. The given ratio is R divided by X. And we have two answer choice options, answer choice, a positive or answer B negative. So to begin this problem, we can start by assessing the sign of R. So that means we need to look at its given expression where we see that both X and Y are squared. So that means with any X value or any Y value inputted into the expression, it will always return a positive value. And therefore we know that R will always be positive. And now we want to look at the sign for X. And again, we are in the second quadrant. So quickly drawing a sketch of the Cartesian coordinate system, we have a vertical line which represents the Y axis as well as a horizontal line that represents our X axis. And we are in the second quadrant. So we are in the top left square of our coordinate system. And here we can see that along the Y axis, we will only have positive Y values. However, along the X axis, we are on the negative X axis. So we will only have negative X values. So again, X is always going to be negative. And now looking back at our ratio, we have R divided by X so R is positive. So we will have a positive divided by X which we determined is always negative. So we have a positive divided by a negative. So our given ratio will always be negative and therefore 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.) III , r/y

Key Concepts

Quadrants of the Cartesian Plane

Trigonometric Ratios

Distance Formula and Radius

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