Find the distance between the following pairs of points
(0,-3),(0,7)

Answer

To find the distance between the points (0, -3) and (0, 7), we will use the distance formula. The distance formula states that the distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

### Step-by-Step Solution:

1. **Identify the coordinates of the points**:
- Let point A be \( (x_1, y_1) = (0, -3) \)
- Let point B be \( (x_2, y_2) = (0, 7) \)

2. **Substitute the coordinates into the distance formula**:
\[ d = \sqrt{(0 - 0)^2 + (7 - (-3))^2} \]

3. **Calculate the differences**:
- For the x-coordinates: \( 0 - 0 = 0 \)
- For the y-coordinates: \( 7 - (-3) = 7 + 3 = 10 \)

4. **Substitute the differences back into the formula**:
\[ d = \sqrt{(0)^2 + (10)^2} \]

5. **Calculate the squares**:
\[ d = \sqrt{0 + 100} \]

6. **Simplify the expression**:
\[ d = \sqrt{100} = 10 \]

### Final Answer:
The distance between the points (0, -3) and (0, 7) is \( 10 \).

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