Point `P(6,-4)` lies in which quadrant?

Options

A. First
B. Second
C. Third
D. Fourth.

Answer

To determine in which quadrant the point \( P(6, -4) \) lies, we can follow these steps:

### Step 1: Understand the Coordinate System
The coordinate system is divided into four quadrants:
- **Quadrant I**: \( x > 0 \) and \( y > 0 \)
- **Quadrant II**: \( x < 0 \) and \( y > 0 \)
- **Quadrant III**: \( x < 0 \) and \( y < 0 \)
- **Quadrant IV**: \( x > 0 \) and \( y < 0 \)

### Step 2: Identify the Coordinates
The point \( P(6, -4) \) has:
- \( x \) coordinate = 6 (which is positive)
- \( y \) coordinate = -4 (which is negative)

### Step 3: Determine the Quadrant
Since the \( x \) coordinate is positive and the \( y \) coordinate is negative, the point \( P(6, -4) \) lies in **Quadrant IV**.

### Conclusion
Thus, the point \( P(6, -4) \) lies in the fourth quadrant.

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