To find the midpoint of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the midpoint formula:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((5, +\infty)\)[/tex]:
1. Identify the coordinates of the endpoints:
[tex]\[
(x_1, y_1) = (3.5, 2.2)
\][/tex]
[tex]\[
(x_2, y_2) = (5, +\infty)
\][/tex]
2. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{3.5 + 5}{2} = \frac{8.5}{2} = 4.25
\][/tex]
3. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{2.2 + (+\infty)}{2} = \text{undefined}
\][/tex]
Due to the presence of [tex]\(+\infty\)[/tex] as the [tex]\(y\)[/tex]-coordinate of one endpoint, adding it to any number and then dividing by 2 results in [tex]\(+\infty\)[/tex], making it impossible to calculate a finite midpoint.
Thus, the midpoint cannot be defined correctly in this case.
Answer:
[tex]\[
\boxed{\text{The midpoint cannot be calculated because one endpoint has an infinite coordinate.}}
\][/tex]
