Find the distance of the point P(-4,3,5) from coordinate axes.

Answer

To find the distance of the point P(-4, 3, 5) from the coordinate axes, we will calculate the distances from the x-axis, y-axis, and z-axis separately using the appropriate formulas.

### Step-by-Step Solution:

1. **Distance from the x-axis**:
The distance of a point from the x-axis is calculated using the formula:
\[ D = \sqrt{y^2 + z^2} \]
For the point P(-4, 3, 5), the coordinates are:
- \(y = 3\)
- \(z = 5\)

Plugging in the values:
\[ D = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} \]
Thus, the distance from the x-axis is \(\sqrt{34}\).

2. **Distance from the y-axis**:
The distance of a point from the y-axis is calculated using the formula:
\[ D = \sqrt{x^2 + z^2} \]
For the point P(-4, 3, 5), the coordinates are:
- \(x = -4\)
- \(z = 5\)

Plugging in the values:
\[ D = \sqrt{(-4)^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \]
Thus, the distance from the y-axis is \(\sqrt{41}\).

3. **Distance from the z-axis**:
The distance of a point from the z-axis is calculated using the formula:
\[ D = \sqrt{x^2 + y^2} \]
For the point P(-4, 3, 5), the coordinates are:
- \(x = -4\)
- \(y = 3\)

Plugging in the values:
\[ D = \sqrt{(-4)^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} \]
Thus, the distance from the z-axis is \(5\).

### Final Results:
- Distance from the x-axis: \(\sqrt{34}\)
- Distance from the y-axis: \(\sqrt{41}\)
- Distance from the z-axis: \(5\)