Point `P(-3, -4)` lies in which quadrant?

Options

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

Answer

To determine in which quadrant the point \( P(-3, -4) \) lies, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Coordinate System**:
- The Cartesian coordinate system is divided into four quadrants:
- **1st Quadrant**: \( x > 0 \) and \( y > 0 \)
- **2nd Quadrant**: \( x < 0 \) and \( y > 0 \)
- **3rd Quadrant**: \( x < 0 \) and \( y < 0 \)
- **4th Quadrant**: \( x > 0 \) and \( y < 0 \)

2. **Identify the Coordinates of Point P**:
- The coordinates of point \( P \) are given as \( (-3, -4) \).
- Here, \( x = -3 \) and \( y = -4 \).

3. **Determine the Signs of x and y**:
- Since \( x = -3 \) (which is less than 0) and \( y = -4 \) (which is also less than 0), both coordinates are negative.

4. **Locate the Quadrant**:
- According to the quadrant definitions:
- Both \( x \) and \( y \) are negative, which means point \( P(-3, -4) \) lies in the **3rd Quadrant**.

5. **Conclusion**:
- Therefore, point \( P(-3, -4) \) lies in the **3rd Quadrant**.