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

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/r

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. And we need to note that R is equivalent to the square root of X squared plus Y squared. We are given the ratio X divided by R and 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 need to look at the signs of X and R relative to our given point. So we can start with the sign for R by assessing the expression given for R. And here we can see that both X and Y are squared in the expression. So that tells us that any value we input into this expression will return positive since it must be squared. And so that tells us that R overall will always be positive. So now moving on to our sign for X, we need to draw out our Cartesian plane where we have a vertical line representing the Y axis and then a horizontal line representing the X axis. And we are told that our point XY is in the third quadrant. So we need to recall that the third quadrant is the bottom left box or square of our plane. And so looking at the third quadrant, we can see that we are along the negative X axis and we are also along the negative Y axis. So since we are only paying attention in this expression or ratio to the X sign, we see here that X is always going to be negative since we are in the third quadrant. So now looking back at our ratio again, we have X divided by R so we know X again is always negative and then R is always going to be positive. So we have a negative divided by a positive which just gives us a negative ratio. And therefore we are left with answer choice B where again our 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.) IV , x/r

Key Concepts

Coordinate Plane Quadrants

Distance from Origin (r)

Sign of Ratios in Trigonometry

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