If x>0 and y<0, then the point `(x, -y)` lies in

Options

A. I quadrant
B. II quadrant
C. III quadrant
D. IV quadrant

Answer

To determine the quadrant in which the point \((x, -y)\) lies, given the conditions \(x > 0\) and \(y < 0\), we can follow these steps:

### Step 1: Understand the conditions
We are given:
- \(x > 0\): This means that the x-coordinate is positive.
- \(y < 0\): This means that the y-coordinate is negative.

### Step 2: Analyze the point \((x, -y)\)
The point we need to analyze is \((x, -y)\). Here, we need to determine the sign of \(-y\):
- Since \(y < 0\), when we take the negative of \(y\) (i.e., \(-y\)), it will become positive. This is because the negative of a negative number is positive.

### Step 3: Determine the coordinates of the point
Now we have:
- The x-coordinate is \(x\), which is positive (\(x > 0\)).
- The y-coordinate is \(-y\), which is also positive (\(-y > 0\)).

### Step 4: Identify the quadrant
In coordinate geometry, the quadrants are defined as follows:
- **First Quadrant**: Both coordinates (x, y) are positive.
- **Second Quadrant**: x is negative, y is positive.
- **Third Quadrant**: Both coordinates are negative.
- **Fourth Quadrant**: x is positive, y is negative.

Since both \(x\) and \(-y\) are positive, the point \((x, -y)\) lies in the **First Quadrant**.

### Conclusion
Thus, the point \((x, -y)\) lies in the **First Quadrant**.

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