Suppose that the point \( (x, y) \) is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that \( r=\sqrt{x^{2}+y^{2}} \). III, Choose whether the given ratio is positive or negative. Nogative Positive

In the third quadrant, both x and y coordinates are negative, which means that when we compute the ratio of y to x (i.e., \( \frac{y}{x} \)), we are dividing a negative number by another negative number. This leads to a positive result, as the negatives cancel each other out. Therefore, the ratio is positive. However, if you consider the ratio of y to r or x to r, it will still be based on the same principle. Since r is always positive (being the square root of a sum of squares), the ratio involving r, like \( \frac{y}{r} \) or \( \frac{x}{r} \) in the third quadrant will thus yield a negative result because y and x are both negative. Nonetheless, if referencing just \( \frac{y}{x} \) specifically, consider it positively in context.