The point (-2,-3,-4) lies in the

Options

A. first octant
B. seventh octant
C. second octant
D. eighth octant

Answer

To determine in which quadrant the point (-2, -3, -4) lies, we will analyze the signs of the coordinates (x, y, z).

### Step-by-step Solution:

1. **Identify the coordinates**: The point given is (-2, -3, -4). Here, x = -2, y = -3, and z = -4.

2. **Determine the signs of the coordinates**:
- The x-coordinate is -2 (negative).
- The y-coordinate is -3 (negative).
- The z-coordinate is -4 (negative).

3. **Refer to the quadrant definitions**:
- In three-dimensional geometry, the quadrants are defined based on the signs of the coordinates:
- **1st Quadrant**: (x > 0, y > 0, z > 0)
- **2nd Quadrant**: (x < 0, y > 0, z > 0)
- **3rd Quadrant**: (x < 0, y < 0, z > 0)
- **4th Quadrant**: (x > 0, y < 0, z > 0)
- **5th Quadrant**: (x > 0, y > 0, z < 0)
- **6th Quadrant**: (x < 0, y > 0, z < 0)
- **7th Quadrant**: (x < 0, y < 0, z < 0)
- **8th Quadrant**: (x > 0, y < 0, z < 0)

4. **Identify the quadrant for the given point**:
- Since all three coordinates (x, y, z) are negative (x < 0, y < 0, z < 0), the point (-2, -3, -4) lies in the **7th Quadrant**.

### Conclusion:
The point (-2, -3, -4) lies in the 7th Quadrant.

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