Question

fy the following points.
emilio states that the coordinates $(-\frac{2}{3},\frac{5}{4})$ is in quadrant 3. vince disagrees and says that it is in quadrant 2. are either of them, correct? explain your reasoning.
□ emilio is
□ vince is
□ neither are
correct. the coordinates $(-\frac{2}{3},\frac{5}{4})$ are in
□ quadrant 1
□ quadrant 2
□ quadrant 3
□ quadrant 4
□ x - coordinate is negative, and the y - coordinate is positive.
□ x - coordinate is positive, and the y - coordinate is negative.
because the
□ x - coordinate is negative, and the y - coordinate is negative.
□ x - coordinate is positive, and the y - coordinate is positive.

Explanation:

Step1: Recall quadrant rules

In a Cartesian - coordinate system, in Quadrant 1, \(x>0\) and \(y > 0\); in Quadrant 2, \(x<0\) and \(y>0\); in Quadrant 3, \(x < 0\) and \(y<0\); in Quadrant 4, \(x>0\) and \(y<0\).

Step2: Analyze the given coordinates

For the point \((-\frac{2}{3},\frac{5}{4})\), the \(x\) - coordinate \(x =-\frac{2}{3}<0\) and the \(y\) - coordinate \(y=\frac{5}{4}>0\).

Step3: Determine the quadrant

Since \(x<0\) and \(y > 0\), the point \((-\frac{2}{3},\frac{5}{4})\) is in Quadrant 2.

Answer:

Vince is correct. The coordinates \((-\frac{2}{3},\frac{5}{4})\) are in Quadrant 2 because the x - coordinate is negative, and the y - coordinate is positive.