Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) II , y/x

검증된 단계별 안내

Recall that the ratio given is \( \frac{y}{x} \), where \(x\) and \(y\) are the coordinates of a point in the plane.

Identify the signs of \(x\) and \(y\) in Quadrant II. In this quadrant, \(x < 0\) (negative) and \(y > 0\) (positive).

Since \(y\) is positive and \(x\) is negative, the ratio \( \frac{y}{x} \) is a positive number divided by a negative number.

Dividing a positive number by a negative number results in a negative value, so \( \frac{y}{x} < 0 \) in Quadrant II.

Therefore, the ratio \( \frac{y}{x} \) is negative when the point \((x, y)\) lies in Quadrant II.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Coordinate Plane Quadrants

The coordinate plane is divided into four quadrants, each with specific signs for x and y coordinates. In Quadrant II, x is negative and y is positive. Understanding the sign of coordinates in each quadrant helps determine the sign of ratios like y/x.

Sign of Ratios in Different Quadrants

The sign of a ratio such as y/x depends on the signs of y and x individually. Since y is positive and x is negative in Quadrant II, the ratio y/x will be negative. This concept is crucial for evaluating trigonometric ratios based on point location.

Distance from Origin (r = √(x² + y²))

The distance r from the origin to the point (x, y) is always positive and is calculated using the Pythagorean theorem. While r is not directly needed to find the sign of y/x, it is fundamental in defining trigonometric functions and understanding the point's position.