To find the midpoint of the line segment with endpoints \((2, -5)\) and \((-6, 4)\), you can use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, \((x_1, y_1) = (2, -5)\) and \((x_2, y_2) = (-6, 4)\).
Calculating the x-coordinate of the midpoint:
\[ \frac{x_1 + x_2}{2} = \frac{2 + (-6)}{2} = \frac{2 - 6}{2} = \frac{-4}{2} = -2 \]
Now calculating the y-coordinate of the midpoint:
\[ \frac{y_1 + y_2}{2} = \frac{-5 + 4}{2} = \frac{-1}{2} = -0.5 \]
Thus, the midpoint \(M\) is \((-2, -0.5)\).
So, the correct ordered pair is:
\[ \boxed{(-2, -0.5)} \]