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

Options

A. I octant
B. VI octant
C. II octant
D. V octant

Answer

To determine the octant in which the point (-2, 3, 4) lies, we can follow these steps:

### Step-by-Step Solution:

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

2. **Determine the Signs of the Coordinates**:
- The x-coordinate is negative (x < 0).
- The y-coordinate is positive (y > 0).
- The z-coordinate is positive (z > 0).

3. **Refer to Octant Definitions**:
- The octants in three-dimensional space are defined based on the signs of the coordinates:
- **First Octant**: (x > 0, y > 0, z > 0)
- **Second Octant**: (x < 0, y > 0, z > 0)
- **Third Octant**: (x < 0, y < 0, z > 0)
- **Fourth Octant**: (x > 0, y < 0, z > 0)
- **Fifth Octant**: (x > 0, y > 0, z < 0)
- **Sixth Octant**: (x < 0, y > 0, z < 0)
- **Seventh Octant**: (x < 0, y < 0, z < 0)
- **Eighth Octant**: (x > 0, y < 0, z < 0)

4. **Match the Signs to the Octant**:
- From the signs we determined:
- x is negative
- y is positive
- z is positive
- This matches the definition of the **Second Octant**.

5. **Conclusion**: Therefore, the point (-2, 3, 4) lies in the **Second Octant**.