Question 8, 1.3.39 HW Score SG84\%, 7 of 19 pow Pontssoof 1 Suppose that the point \( (x, y) \) is in the indicated quadrant. Decide whether the given ratio is positive or negative. Recall that \( \mathrm{r}=\sqrt{x^{2}+y^{2}} \). \( 1 \frac{y}{8} \) In Quadrant \( L \) is \( \frac{y}{r} \) positive or negative? Positive Negative

In the context of coordinate quadrants, let's clarify the signs of \( y \) and \( r \) in each quadrant to determine whether the ratio \( \frac{y}{r} \) is positive or negative. ### Understanding the Quadrants: 1. **Quadrant I**: - \( x > 0 \) - \( y > 0 \) - \( r = \sqrt{x^2 + y^2} > 0 \) - **\( \frac{y}{r} \)**: Positive 2. **Quadrant II**: - \( x < 0 \) - \( y > 0 \) - \( r = \sqrt{x^2 + y^2} > 0 \) - **\( \frac{y}{r} \)**: Positive 3. **Quadrant III**: - \( x < 0 \) - \( y < 0 \) - \( r = \sqrt{x^2 + y^2} > 0 \) - **\( \frac{y}{r} \)**: Negative 4. **Quadrant IV**: - \( x > 0 \) - \( y < 0 \) - \( r = \sqrt{x^2 + y^2} > 0 \) - **\( \frac{y}{r} \)**: Negative ### Applying to Your Question: Assuming **Quadrant I** (since "Quadrant L" seems like a typo and Quadrant I is the first quadrant): - Both \( y \) and \( r \) are positive. - Therefore, \( \frac{y}{r} \) is **positive**. So, **in Quadrant I, \( \frac{y}{r} \) is positive**. **Answer:** Positive