To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the given endpoints are [tex]\((3.5, 2.2)\)[/tex] and [tex]\((7.5, -4.8)\)[/tex].
We need to find the x-coordinate of the midpoint:
[tex]\[
\frac{3.5 + 7.5}{2}
\][/tex]
First, add the x-coordinates:
[tex]\[
3.5 + 7.5 = 11
\][/tex]
Next, divide by 2:
[tex]\[
\frac{11}{2} = 5.5
\][/tex]
So, the x-coordinate of the midpoint is [tex]\(5.5\)[/tex].
Now, let's find the y-coordinate of the midpoint:
[tex]\[
\frac{2.2 + (-4.8)}{2}
\][/tex]
First, add the y-coordinates:
[tex]\[
2.2 + (-4.8) = 2.2 - 4.8 = -2.6
\][/tex]
Next, divide by 2:
[tex]\[
\frac{-2.6}{2} = -1.3
\][/tex]
So, the y-coordinate of the midpoint is [tex]\(-1.3\)[/tex].
Therefore, the coordinates of the midpoint of the line segment with endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((7.5, -4.8)\)[/tex] are:
[tex]\[
(5.5, -1.3)
\][/tex]
Given the options:
A. [tex]\((2.5, -2.6)\)[/tex]
B. [tex]\((2.5, -1.3)\)[/tex]
C. [tex]\((5, -1.3)\)[/tex]
D. [tex]\((5, -2.6)\)[/tex]
The correct answer is not listed among the options as the correct coordinates are [tex]\((5.5, -1.3)\)[/tex].
