To find the distance between the points A(2, 3) and B(7, 8), 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 \((x_2, y_2) = (7, 8)\).
First, we subtract the coordinates:
\[ x_2 - x_1 = 7 - 2 = 5 \] \[ y_2 - y_1 = 8 - 3 = 5 \]
Now, we can substitute these values into the distance formula:
\[ d = \sqrt{(5)^2 + (5)^2} \] \[ d = \sqrt{25 + 25} \] \[ d = \sqrt{50} \] \[ d = 5\sqrt{2} \]
So the distance between points A and B is \(5\sqrt{2}\).
Among the options given, \(5\sqrt{2}\) is the correct response.