Name the octant in which (-4, -3, -8) lies.

Answer

To determine the octant in which the point (-4, -3, -8) lies, we can follow these steps:

### Step 1: Identify the Coordinates
The given point is (-4, -3, -8). Here, the coordinates are:
- x = -4
- y = -3
- z = -8

### Step 2: Determine the Signs of the Coordinates
Next, we analyze the signs of each coordinate:
- The x-coordinate is negative (-4).
- The y-coordinate is negative (-3).
- The z-coordinate is negative (-8).

### Step 3: Understand the Octants in 3D Space
In three-dimensional geometry, the space is divided into eight octants based on the signs of the coordinates:
1. **1st Octant**: (x > 0, y > 0, z > 0)
2. **2nd Octant**: (x < 0, y > 0, z > 0)
3. **3rd Octant**: (x < 0, y < 0, z > 0)
4. **4th Octant**: (x > 0, y < 0, z > 0)
5. **5th Octant**: (x > 0, y > 0, z < 0)
6. **6th Octant**: (x < 0, y > 0, z < 0)
7. **7th Octant**: (x < 0, y < 0, z < 0)
8. **8th Octant**: (x > 0, y < 0, z < 0)

### Step 4: Match the Signs to the Octants
From the signs of the coordinates:
- x is negative,
- y is negative,
- z is negative.

This combination corresponds to the **7th Octant** where all coordinates are negative (x < 0, y < 0, z < 0).

### Conclusion
Thus, the point (-4, -3, -8) lies in the **7th Octant**.

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