Question 6, 1.3.31 HW Score: 26.32\%, 5 of 19 points Points: 0 of 1 Suppose that the point \( (x, y) \) is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that \( r=\sqrt{x^{2}+y^{2}} \). \[ 1, \frac{r}{y} \] In Quadrant I, is \( \frac{r}{y} \) positive or negative? Negative Positive

In **Quadrant I**, both \( x \) and \( y \) coordinates of a point \( (x, y) \) are **positive**. Given the ratio: \[ \frac{r}{y} \] where \( r = \sqrt{x^{2} + y^{2}} \), let's analyze the sign of this ratio. 1. **\( r \) is always positive**: \[ r = \sqrt{x^{2} + y^{2}} > 0 \quad \text{(since both \( x \) and \( y \) are positive in Quadrant I)} \] 2. **\( y \) is positive in Quadrant I**: \[ y > 0 \] 3. **The ratio \( \frac{r}{y} \)**: \[ \frac{r}{y} = \frac{\text{Positive}}{\text{Positive}} = \text{Positive} \] Therefore, **\( \frac{r}{y} \) is positive in Quadrant I**. **Answer:** Positive