To find the midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\((-5.5, -6.1)\)[/tex] and [tex]\((-0.5, 9.1)\)[/tex]:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-5.5 + (-0.5)}{2} = \frac{-5.5 - 0.5}{2} = \frac{-6.0}{2} = -3.0
\][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{-6.1 + 9.1}{2} = \frac{3.0}{2} = 1.5
\][/tex]
Thus, the midpoint of the line segment is [tex]\((-3.0, 1.5)\)[/tex].
Among the given options:
A. [tex]\((-3, 3)\)[/tex]
B. [tex]\((-6, 3)\)[/tex]
C. [tex]\((-3, 1.5)\)[/tex]
D. [tex]\((-6, 1.5)\)[/tex]
The correct answer is:
C. [tex]\((-3, 1.5)\)[/tex]
