To find the midpoint of a segment defined by two endpoints \((x_1, y_1)\) and \((x_2, y_2)\), you can use the midpoint formula:
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
For the given endpoints \((-10, -7)\) and \((-4, -4)\), we have:
\[ x_1 = -10, \quad y_1 = -7, \quad x_2 = -4, \quad y_2 = -4 \]
Now, substitute these values into the midpoint formula:
\[ \text{Midpoint} = \left( \frac{-10 + (-4)}{2}, \frac{-7 + (-4)}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{-10 - 4}{2} = \frac{-14}{2} = -7 \]
Calculating the y-coordinate:
\[ \frac{-7 - 4}{2} = \frac{-11}{2} = -5.5 \]
Thus, the midpoint of the segment is:
\[ \boxed{(-7, -5.5)} \]