To determine the midpoint of the line segment [tex]\(\overline{A B}\)[/tex] with endpoints [tex]\(A(9,8)\)[/tex] and [tex]\(B(-1,-2)\)[/tex], we will use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step-by-step:
1. Identify the coordinates of endpoints [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
- [tex]\(A(9, 8)\)[/tex]
- [tex]\(B(-1, -2)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_x = \frac{9 + (-1)}{2} = \frac{9 - 1}{2} = \frac{8}{2} = 4
\][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_y = \frac{8 + (-2)}{2} = \frac{8 - 2}{2} = \frac{6}{2} = 3
\][/tex]
4. Combine the coordinates to form the midpoint:
[tex]\[
\text{Midpoint} = (4, 3)
\][/tex]
Therefore, the correct answer is:
D. [tex]\((4, 3)\)[/tex]
