To find the midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], you use the midpoint formula:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
For the given endpoints [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. Apply the midpoint formula to find the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_x = \frac{x_1 + x_2}{2} = \frac{-2 + 4}{2} = \frac{2}{2} = 1
\][/tex]
3. Next, apply the midpoint formula to find the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_y = \frac{y_1 + y_2}{2} = \frac{-2 + 6}{2} = \frac{4}{2} = 2
\][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-2, -2)\)[/tex] and [tex]\((4, 6)\)[/tex] is [tex]\((1, 2)\)[/tex].
Thus, the correct answer is:
C. [tex]\((1, 2)\)[/tex]
