Find the distance between the points (0, 6) and (0, -2).

Answer

To find the distance between the points (0, 6) and (0, -2), we can use the distance formula:

### Step-by-step Solution:

1. **Identify the coordinates**:
- Let the first point be \( P_1(0, 6) \) where \( x_1 = 0 \) and \( y_1 = 6 \).
- Let the second point be \( P_2(0, -2) \) where \( x_2 = 0 \) and \( y_2 = -2 \).

2. **Use the distance formula**:
The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

3. **Substitute the values into the formula**:
\[ d = \sqrt{(0 - 0)^2 + (-2 - 6)^2} \]

4. **Calculate the differences**:
- First, calculate \( x_2 - x_1 \):
\[ 0 - 0 = 0 \]
- Then, calculate \( y_2 - y_1 \):
\[ -2 - 6 = -8 \]

5. **Square the differences**:
\[ d = \sqrt{(0)^2 + (-8)^2} = \sqrt{0 + 64} \]

6. **Simplify the expression**:
\[ d = \sqrt{64} \]

7. **Calculate the square root**:
\[ d = 8 \]

### Final Answer:
The distance between the points (0, 6) and (0, -2) is \( 8 \).

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