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