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 will use the distance formula. The distance formula is given by:

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

### Step 1: Identify the coordinates
We have the two points:
- Point 1: \((x_1, y_1) = (7, -7)\)
- Point 2: \((x_2, y_2) = (15, 8)\)

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

\[ d = \sqrt{(15 - 7)^2 + (8 - (-7))^2} \]

### Step 3: Simplify the expressions inside the square root
Calculate \(x_2 - x_1\) and \(y_2 - y_1\):

\[ x_2 - x_1 = 15 - 7 = 8 \]
\[ y_2 - y_1 = 8 - (-7) = 8 + 7 = 15 \]

### Step 4: Substitute these values back into the formula
Now we can substitute these values back into the formula:

\[ d = \sqrt{(8)^2 + (15)^2} \]

### Step 5: Calculate the squares
Calculate \(8^2\) and \(15^2\):

\[ 8^2 = 64 \]
\[ 15^2 = 225 \]

### Step 6: Add the squares
Now add these two results:

\[ d = \sqrt{64 + 225} = \sqrt{289} \]

### Step 7: Calculate the square root
Finally, we find the square root of 289:

\[ d = 17 \]

### Conclusion
The distance between the coordinates (7, -7) and (15, 8) is \(17\).

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