Find the foot of perpendicular drawn from a point P(2, 4, -5) on the coordinate planes.

Answer

To find the foot of the perpendicular drawn from the point \( P(2, 4, -5) \) to the coordinate planes, we will consider each coordinate plane separately: the XY-plane, YZ-plane, and XZ-plane.

### Step-by-Step Solution:

1. **Foot of the Perpendicular on the XY-plane:**
- The XY-plane is defined by \( z = 0 \).
- To find the foot of the perpendicular from point \( P(2, 4, -5) \) to the XY-plane, we keep the x and y coordinates the same and set the z coordinate to 0.
- Therefore, the foot of the perpendicular on the XY-plane is:
\[ F_{XY} = (2, 4, 0) \]

2. **Foot of the Perpendicular on the YZ-plane:**
- The YZ-plane is defined by \( x = 0 \).
- To find the foot of the perpendicular from point \( P(2, 4, -5) \) to the YZ-plane, we set the x coordinate to 0 while keeping the y and z coordinates the same.
- Therefore, the foot of the perpendicular on the YZ-plane is:
\[ F_{YZ} = (0, 4, -5) \]

3. **Foot of the Perpendicular on the XZ-plane:**
- The XZ-plane is defined by \( y = 0 \).
- To find the foot of the perpendicular from point \( P(2, 4, -5) \) to the XZ-plane, we set the y coordinate to 0 while keeping the x and z coordinates the same.
- Therefore, the foot of the perpendicular on the XZ-plane is:
\[ F_{XZ} = (2, 0, -5) \]

### Summary of Results:
- Foot of the perpendicular on the XY-plane: \( (2, 4, 0) \)
- Foot of the perpendicular on the YZ-plane: \( (0, 4, -5) \)
- Foot of the perpendicular on the XZ-plane: \( (2, 0, -5) \)