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

Answer

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Answer

$\boxed{\text{Final Answer: Positive}}$

Steps

Step 1 ：Suppose that the point $(x, y)$ is in the indicated quadrant N (or the first quadrant).

Step 2 ：Recall that $r=\sqrt{x^{2}+y^{2}}$ and is always positive.

Step 3 ：In quadrant N, both $x$ and $y$ are positive.

Step 4 ：Therefore, the sign of the ratio $\frac{r}{x}$ will depend on the sign of $x$.

Step 5 ：Since $x$ is positive in quadrant N, the ratio $\frac{r}{x}$ will be positive.

Step 6 ：$\boxed{\text{Final Answer: Positive}}$