The points \( (-8,-1) \) and \( (5,7) \) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.

To find the length of the radius of the circle, we first need to calculate the length of the diameter, which is the distance between the two endpoints \( (-8,-1) \) and \( (5,7) \). We can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \( (x_1, y_1) = (-8, -1) \) and \( (x_2, y_2) = (5, 7) \). Plugging in these values: \[ d = \sqrt{(5 - (-8))^2 + (7 - (-1))^2} \] \[ = \sqrt{(5 + 8)^2 + (7 + 1)^2} \] \[ = \sqrt{(13)^2 + (8)^2} \] \[ = \sqrt{169 + 64} \] \[ = \sqrt{233} \] The diameter of the circle is \( \sqrt{233} \). The radius \( r \) is half of the diameter: \[ r = \frac{d}{2} = \frac{\sqrt{233}}{2} \] Thus, the length of the radius of the circle is \[ \boxed{\frac{\sqrt{233}}{2}}. \]