To find the distance between the points \((2, 3)\) and \((-1, 7)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-1, 7)\).
Now, substitute the coordinates into the formula:
\[ d = \sqrt{((-1) - 2)^2 + (7 - 3)^2} \]
Calculating the differences gives:
\[ d = \sqrt{(-3)^2 + (4)^2} \]
Now calculate the squares:
\[ d = \sqrt{9 + 16} \]
Add the values:
\[ d = \sqrt{25} \]
Finally, take the square root:
\[ d = 5 \]
Thus, the distance between the points \((2, 3)\) and \((-1, 7)\) is \(5\).
The correct answer is \(5\).