Find the distances of the point (-4, 3, 6) from the coordinate planes.
[Hint : Distance cannot be negative.]

Answer

To find the distances of the point (-4, 3, 6) from the coordinate planes, we need to understand how distances are calculated from each of the three coordinate planes: the XY-plane, the YZ-plane, and the XZ-plane.

1. **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, 6), the z-coordinate is 6.
- Therefore, the distance from the XY-plane is:
\[ \text{Distance}_{XY} = |z| = |6| = 6 \]

2. **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, 6), the x-coordinate is -4.
- Therefore, the distance from the YZ-plane is:
\[ \text{Distance}_{YZ} = |x| = |-4| = 4 \]

3. **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, 6), the y-coordinate is 3.
- Therefore, the distance from the XZ-plane is:
\[ \text{Distance}_{XZ} = |y| = |3| = 3 \]

In summary, the distances from the point (-4, 3, 6) to the coordinate planes are:
- Distance from the XY-plane: 6
- Distance from the YZ-plane: 4
- Distance from the XZ-plane: 3

### Final Answer:
- Distance from XY-plane: 6
- Distance from YZ-plane: 4
- Distance from XZ-plane: 3