Find the distance of the point (-3, -4, 6) from z-axis.

Answer

To find the distance of the point (-3, -4, 6) from the z-axis, we can follow these steps:

### Step 1: Understand the concept of distance from the z-axis
The distance of a point from the z-axis can be calculated using the formula:
\[ d = \sqrt{x^2 + y^2} \]
where \( (x, y, z) \) are the coordinates of the point.

### Step 2: Identify the coordinates of the point
The given point is \( (-3, -4, 6) \). Here, \( x = -3 \) and \( y = -4 \).

### Step 3: Substitute the x and y values into the distance formula
Now, we substitute \( x \) and \( y \) into the distance formula:
\[ d = \sqrt{(-3)^2 + (-4)^2} \]

### Step 4: Calculate the squares of x and y
Calculating the squares:
\[ (-3)^2 = 9 \]
\[ (-4)^2 = 16 \]

### Step 5: Add the squares
Now, add the squares together:
\[ d = \sqrt{9 + 16} \]

### Step 6: Simplify the expression
Combine the values:
\[ d = \sqrt{25} \]

### Step 7: Calculate the square root
Finally, calculate the square root:
\[ d = 5 \]

### Final Answer
The distance of the point (-3, -4, 6) from the z-axis is \( 5 \).

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