To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint formula is:
[tex]\[
\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the endpoints.
Given the endpoints [tex]\((-2, -2)\)[/tex] and [tex]\( (4, 6) \)[/tex], we can identify [tex]\( x_1 = -2 \)[/tex], [tex]\( y_1 = -2 \)[/tex], [tex]\( x_2 = 4 \)[/tex], and [tex]\( y_2 = 6 \)[/tex].
Let's apply these values to the midpoint formula step by step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-2 + 4}{2} = \frac{2}{2} = 1
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{-2 + 6}{2} = \frac{4}{2} = 2
\][/tex]
So, the midpoint of the line segment is:
[tex]\[
(1, 2)
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{(1, 2)} \)[/tex].
