To determine the midpoint of the line segment [tex]\(\overline{AB}\)[/tex] with given endpoints [tex]\(A(9,8)\)[/tex] and [tex]\(B(-1,-2)\)[/tex], we can use the midpoint formula. The midpoint formula is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\(A\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\(B\)[/tex].
Let's substitute the given coordinates into the formula. For point [tex]\(A\)[/tex], [tex]\(x_1 = 9\)[/tex] and [tex]\(y_1 = 8\)[/tex]. For point [tex]\(B\)[/tex], [tex]\(x_2 = -1\)[/tex] and [tex]\(y_2 = -2\)[/tex].
Now calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{9 + (-1)}{2} = \frac{9 - 1}{2} = \frac{8}{2} = 4
\][/tex]
Next, calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{8 + (-2)}{2} = \frac{8 - 2}{2} = \frac{6}{2} = 3
\][/tex]
Thus, the midpoint of [tex]\(\overline{AB}\)[/tex] is:
[tex]\[
(4, 3)
\][/tex]
Therefore, the correct answer is:
D. [tex]\((4, 3)\)[/tex]
