Find the distance between the coordinates (7, -7) and (15, 8).

Options

A. 13
B. 15
C. 17
D. 12

Answer

To find the distance between the coordinates (7, -7) and (15, 8), we can use the distance formula. 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**:
- Let point A be \((x_1, y_1) = (7, -7)\)
- Let point B be \((x_2, y_2) = (15, 8)\)

2. **Substitute the coordinates into the distance formula**:
\[ d = \sqrt{(15 - 7)^2 + (8 - (-7))^2} \]

3. **Calculate the differences**:
- \(x_2 - x_1 = 15 - 7 = 8\)
- \(y_2 - y_1 = 8 - (-7) = 8 + 7 = 15\)

4. **Square the differences**:
\[ d = \sqrt{(8)^2 + (15)^2} \]
\[ d = \sqrt{64 + 225} \]

5. **Add the squared values**:
\[ d = \sqrt{289} \]

6. **Calculate the square root**:
\[ d = 17 \]

### Final Answer:
The distance between the coordinates (7, -7) and (15, 8) is **17 units**.