### Part I
To find the midpoint of a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the formula:
[tex]\[ \text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \][/tex]
So, the correct choice is:
[tex]\[
\begin{tabular}{|l|l|}
\hline A. $\left(x_1-x_2, y_1-y_2\right)$ & B. $\left(x_1+x_2, y_1+y_2\right)$ \\
\hline C. $\left(\frac{x_1-x_2}{2}, \frac{y_1-y_2}{2}\right)$ & \(\boxed{\text{D. } \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)} \) \\
\hline
\end{tabular}
\][/tex]
### Part II
Now, we will use the formula from Part I to find the midpoint of the segment with endpoints [tex]\((-2, -1)\)[/tex] and [tex]\((0, 9)\)[/tex].
Step-by-Step Solution:
1. Identify the coordinates of the endpoints:
- [tex]\( (x_1, y_1) = (-2, -1) \)[/tex]
- [tex]\( (x_2, y_2) = (0, 9) \)[/tex]
2. Substitute the coordinates into the midpoint formula:
[tex]\[ \text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \][/tex]
3. Plugging in the values:
[tex]\[ \text{Midpoint} = \left(\frac{-2 + 0}{2}, \frac{-1 + 9}{2}\right) \][/tex]
4. Simplify the expressions inside the parentheses:
- For the x-coordinate:
[tex]\[ \frac{-2 + 0}{2} = \frac{-2}{2} = -1.0 \][/tex]
- For the y-coordinate:
[tex]\[ \frac{-1 + 9}{2} = \frac{8}{2} = 4.0 \][/tex]
5. Therefore, the midpoint of the segment is:
[tex]\[ \left(-1.0, 4.0\right) \][/tex]
So, the final answer, showing all work, is:
The midpoint of the segment with endpoints [tex]\((-2, -1)\)[/tex] and [tex]\((0, 9)\)[/tex] is [tex]\(\boxed{(-1.0, 4.0)}\)[/tex].
