The distance between x-axis and the point (3, 12, 5) is

Options

A. A. 31 units
B. B. 13 units
C. C. 10 units
D. D. 9 units

Answer

To find the distance between the x-axis and the point (3, 12, 5), we can follow these steps:

### Step 1: Understand the coordinates
The point given is (3, 12, 5). Here, the coordinates are:
- x = 3
- y = 12
- z = 5

### Step 2: Identify the formula for the distance from the x-axis
The distance \( d \) from a point (x, y, z) to the x-axis can be calculated using the formula:
\[ d = \sqrt{y^2 + z^2} \]
This formula is derived from the Pythagorean theorem, considering the y and z coordinates as the legs of a right triangle.

### Step 3: Substitute the values into the formula
Now, we substitute the values of y and z into the formula:
\[ d = \sqrt{12^2 + 5^2} \]

### Step 4: Calculate the squares
Calculate \( 12^2 \) and \( 5^2 \):
\[ 12^2 = 144 \]
\[ 5^2 = 25 \]

### Step 5: Add the squares
Now, add the two results:
\[ d = \sqrt{144 + 25} = \sqrt{169} \]

### Step 6: Calculate the square root
Finally, calculate the square root:
\[ d = 13 \]

### Final Answer
The distance between the x-axis and the point (3, 12, 5) is **13 units**.

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