To find the midpoint of a line segment with given endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we can use the midpoint formula, which is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex], let's find each component of the midpoint step-by-step.
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{3.2 + 1.6}{2}
\][/tex]
Adding the [tex]\(x\)[/tex]-coordinates:
[tex]\[
3.2 + 1.6 = 4.8
\][/tex]
Now, divide by 2:
[tex]\[
\frac{4.8}{2} = 2.4
\][/tex]
So, the [tex]\(x\)[/tex]-coordinate of the midpoint is [tex]\(2.4\)[/tex].
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{2.5 + (-4.5)}{2}
\][/tex]
Adding the [tex]\(y\)[/tex]-coordinates:
[tex]\[
2.5 + (-4.5) = 2.5 - 4.5 = -2.0
\][/tex]
Now, divide by 2:
[tex]\[
\frac{-2.0}{2} = -1.0
\][/tex]
So, the [tex]\(y\)[/tex]-coordinate of the midpoint is [tex]\(-1\)[/tex].
Therefore, the midpoint of the line segment is:
[tex]\[
(2.4, -1)
\][/tex]
The correct answer is:
B. [tex]\((2.4, -1)\)[/tex]
