To find the midpoint \( M \) of a line segment with endpoints \( G(4, 2) \) and \( H(-6, -6) \), we can use the midpoint formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Where \( (x_1, y_1) \) are the coordinates of point \( G \) and \( (x_2, y_2) \) are the coordinates of point \( H \).
Substituting in the coordinates:
- \( x_1 = 4 \)
- \( y_1 = 2 \)
- \( x_2 = -6 \)
- \( y_2 = -6 \)
Now plug these values into the formula:
\[ M = \left( \frac{4 + (-6)}{2}, \frac{2 + (-6)}{2} \right) \]
Calculating the x-coordinate:
\[ \frac{4 - 6}{2} = \frac{-2}{2} = -1 \]
Calculating the y-coordinate:
\[ \frac{2 - 6}{2} = \frac{-4}{2} = -2 \]
Thus, the coordinates of the midpoint \( M \) are:
\[ M = (-1, -2) \]
So, the final answer is:
\[ M = (-1, -2) \]