To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint [tex]\((x_m, y_m)\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated as follows:
[tex]\[
x_m = \frac{x_1 + x_2}{2}
\][/tex]
[tex]\[
y_m = \frac{y_1 + y_2}{2}
\][/tex]
Given the endpoints [tex]\((-2, -2)\)[/tex] and [tex]\((4, 6)\)[/tex], we can plug these values into the formula:
For [tex]\(x_m\)[/tex]:
[tex]\[
x_m = \frac{-2 + 4}{2} = \frac{2}{2} = 1
\][/tex]
For [tex]\(y_m\)[/tex]:
[tex]\[
y_m = \frac{-2 + 6}{2} = \frac{4}{2} = 2
\][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-2, -2)\)[/tex] and [tex]\((4, 6)\)[/tex] is [tex]\((1, 2)\)[/tex].
So, the correct answer is:
B. [tex]\((1, 2)\)[/tex]
