The Three coordiantes planes divide the space into ……. Parts.

Options

A. 6 parts
B. 8 parts
C. 4 parts
D. None of these

Answer

To determine how many parts the three coordinate planes divide the space into, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Coordinate Planes**:
In a three-dimensional space, there are three coordinate planes: the XY-plane, the YZ-plane, and the XZ-plane. Each of these planes divides the space into different regions.

2. **Visualizing the Planes**:
- The XY-plane is where z = 0.
- The YZ-plane is where x = 0.
- The XZ-plane is where y = 0.
By visualizing these planes, we can see how they intersect.

3. **Counting the Regions**:
Each coordinate plane divides the space into two halves.
- The XY-plane divides the space into the positive z region (above the XY-plane) and the negative z region (below the XY-plane).
- The YZ-plane divides the space into the positive x region (to the right of the YZ-plane) and the negative x region (to the left of the YZ-plane).
- The XZ-plane divides the space into the positive y region (in front of the XZ-plane) and the negative y region (behind the XZ-plane).

4. **Combining the Divisions**:
Since each plane divides the space into two parts, and there are three planes, the total number of regions formed can be calculated as:
\[ 2 \times 2 \times 2 = 8 \]

5. **Conclusion**:
Therefore, the three coordinate planes divide the space into **8 parts**. Each of these parts is known as an **octant**.

### Final Answer:
The three coordinate planes divide the space into **8 parts**.

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