To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The formula for the midpoint [tex]\((M)\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\][/tex]
Given the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/tex], let's substitute these values into the formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_x = \frac{3.5 + 1.5}{2}
\][/tex]
Simplifying inside the parentheses:
[tex]\[
\text{Midpoint}_x = \frac{5}{2}
\][/tex]
Then divide:
[tex]\[
\text{Midpoint}_x = 2.5
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\text{Midpoint}_y = \frac{2.2 + (-4.8)}{2}
\][/tex]
Simplifying inside the parentheses:
[tex]\[
\text{Midpoint}_y = \frac{-2.6}{2}
\][/tex]
Then divide:
[tex]\[
\text{Midpoint}_y = -1.3
\][/tex]
Therefore, the midpoint of the line segment with the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/tex] is [tex]\((2.5, -1.3)\)[/tex].
The correct answer is:
C. [tex]\((2.5, -1.3)\)[/tex]
