Find the distances of the point (-4, -3, 4) from the coordinate planes.
[Hint : Distance cannot be negative.]

Answer

To find the distances of the point (-4, -3, 4) from the coordinate planes, we need to understand the relationship between the coordinates of the point and the planes.

1. **Identify the Coordinate Planes**:
- The three coordinate planes are:
- **XY Plane**: This plane is defined by z = 0.
- **YZ Plane**: This plane is defined by x = 0.
- **XZ Plane**: This plane is defined by y = 0.

2. **Distance from the XY Plane**:
- The distance from a point (x, y, z) to the XY plane is given by the absolute value of the z-coordinate.
- For the point (-4, -3, 4), the z-coordinate is 4.
- Therefore, the distance from the XY plane is:
\[ \text{Distance to XY Plane} = |z| = |4| = 4 \]

3. **Distance from the YZ Plane**:
- The distance from a point (x, y, z) to the YZ plane is given by the absolute value of the x-coordinate.
- For the point (-4, -3, 4), the x-coordinate is -4.
- Therefore, the distance from the YZ plane is:
\[ \text{Distance to YZ Plane} = |x| = |-4| = 4 \]

4. **Distance from the XZ Plane**:
- The distance from a point (x, y, z) to the XZ plane is given by the absolute value of the y-coordinate.
- For the point (-4, -3, 4), the y-coordinate is -3.
- Therefore, the distance from the XZ plane is:
\[ \text{Distance to XZ Plane} = |y| = |-3| = 3 \]

5. **Final Distances**:
- The distances from the point (-4, -3, 4) to the coordinate planes are:
- Distance to XY Plane: 4
- Distance to YZ Plane: 4
- Distance to XZ Plane: 3

Thus, the final answer is:
- Distance to XY Plane: 4
- Distance to YZ Plane: 4
- Distance to XZ Plane: 3