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:
[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], you can plug these values into the formula.
First, find the x-coordinate of the midpoint:
[tex]\[
\frac{3.2 + 1.6}{2}
\][/tex]
Calculate the sum:
[tex]\[
3.2 + 1.6 = 4.8
\][/tex]
Now, divide by 2:
[tex]\[
\frac{4.8}{2} = 2.4
\][/tex]
Next, find the y-coordinate of the midpoint:
[tex]\[
\frac{2.5 + (-4.5)}{2}
\][/tex]
Calculate the sum:
[tex]\[
2.5 + (-4.5) = -2.0
\][/tex]
Now, divide by 2:
[tex]\[
\frac{-2.0}{2} = -1.0
\][/tex]
Thus, the midpoint of the line segment with endpoints [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex] is:
[tex]\[
(2.4, -1.0)
\][/tex]
Among the given options, the correct answer is:
C. [tex]\((2.4, -1)\)[/tex]
