To find the midpoint of a line segment given its endpoints, we use the midpoint formula. The formula for the midpoint [tex]\((M)\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula to the endpoints provided, [tex]\((-2, -2)\)[/tex] and [tex]\((4, 6)\)[/tex]:
1. First, identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-2, -2)\)[/tex]
- [tex]\((x_2, y_2) = (4, 6)\)[/tex]
2. Next, plug the coordinates into the midpoint formula to find the x-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_x = \frac{-2 + 4}{2} = \frac{2}{2} = 1
\][/tex]
3. Now, find the y-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_y = \frac{-2 + 6}{2} = \frac{4}{2} = 2
\][/tex]
4. Combine the x and y coordinates to find the midpoint:
[tex]\[
M = (1, 2)
\][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-2, -2)\)[/tex] and [tex]\((4, 6)\)[/tex] is [tex]\((1, 2)\)[/tex].
So, the correct answer is:
D. [tex]\((1, 2)\)[/tex]
