To find the midpoint \( M \) of the line segment with endpoints \( C(2, -5) \) and \( D(-4, -7) \), you can use the midpoint formula:
\[ M\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
In this case, the coordinates of point \( C \) are \( (x_1, y_1) = (2, -5) \) and the coordinates of point \( D \) are \( (x_2, y_2) = (-4, -7) \).
Now plug these values into the formula:
\[ M\left( \frac{2 + (-4)}{2}, \frac{-5 + (-7)}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{2 - 4}{2} = \frac{-2}{2} = -1 \]
Calculating the y-coordinate:
\[ \frac{-5 - 7}{2} = \frac{-12}{2} = -6 \]
Thus, the midpoint \( M \) of the line segment is:
\[ M(-1, -6) \]
So the coordinates of the midpoint are \( (-1, -6) \).