QuestionDetermine if the ratio $\frac{y}{r}$ is positive or negative for point $(x, y)$ in the first quadrant, where $r=\sqrt{x^{2}+y^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. The point $(x, y)$ is in the first quadrant. . The ratio given is $\frac{y}{r}$ .
3. The value of $r$ is given by $r=\sqrt{x^{}+y^{}}$ .

STEP 2

We first need to understand the characteristics of the first quadrant. In the first quadrant, both $x$ and $y$ are positive.

STEP 3

Now, let's consider the denominator $r$ . Since $r=\sqrt{x^{2}+y^{2}}$ , and both $x$ and $y$ are positive in the first quadrant, $r$ will also be positive.

STEP 4

Given that $y$ is positive (as we are in the first quadrant) and $r$ is positive (as it is the square root of the sum of squares of $x$ and $y$ ), the ratio $\frac{y}{r}$ will be positive.
Therefore, the ratio $\frac{y}{r}$ is positive in the first quadrant.

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