The distance between the points A(0,6) and B(0,-2) is

Options

A. 6
B. 8
C. 4
D. 2

Explanation

To find the distance between the points A(0, 6) and B(0, -2), we will use the distance formula. The distance \( d \) between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is given by:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

### Step 1: Identify the coordinates of the points
The coordinates of point A are \( (0, 6) \) and the coordinates of point B are \( (0, -2) \). Here, we can assign:
- \( x_1 = 0 \), \( y_1 = 6 \)
- \( x_2 = 0 \), \( y_2 = -2 \)

### Step 2: Substitute the coordinates into the distance formula
Now, we substitute the values into the distance formula:

\[ d = \sqrt{(0 - 0)^2 + (-2 - 6)^2} \]

### Step 3: Simplify the expression
Calculating the terms inside the square root:

1. \( (0 - 0)^2 = 0^2 = 0 \)
2. \( (-2 - 6) = -8 \) and then \( (-8)^2 = 64 \)

So, we have:

\[ d = \sqrt{0 + 64} = \sqrt{64} \]

### Step 4: Calculate the square root
Now, we calculate the square root:

\[ d = 8 \]

### Conclusion
The distance between the points A(0, 6) and B(0, -2) is \( 8 \) units.