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 , y/r

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 just need to note that R is equal to the square root of X squared plus Y squared. Our given ratio is Y divided by R and we have two answer choice options, answer choice, a positive or answer B negative. So to begin this problem, we can start by looking at our expression given for R and we see that both X and Y are squared. So we will only return a positive value for R since again, the possible values inputted into the expression will always end up being positive. So again, R is going to be positive. Then now to a assess the sign of why we are given that the point is in the second quadrant. So drawing a quick sketch of the Cartesian coordinate system, we have a vertical line for the Y axis and a horizontal line for the X axis. And we are given that we are in the second quadrant. So this is the top left section of our coordinate system. So we can see here that we are in the negative X axis. So we will only have negative X values. However, we are in the positive Y axis. So we will only have positive Y values. So we know from this graph here we are in the second quadrant, so Y will always be positive. And so now looking back at our ratio, we have Y divided by R so we have a positive term over a positive term and this will only ever give us a positive ratio. So we are left with answer choice A where again our give ratio is positive. 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 , y/r

Key Concepts

Quadrants of the Cartesian Plane

Trigonometric Ratios

Pythagorean Theorem and Radius

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