To find the midpoint of the line segment with endpoints [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex], we use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, we have the coordinates [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex].
First, calculate the x-coordinate of the midpoint:
[tex]\[
x_{\text{midpoint}} = \frac{10 + 3}{2} = \frac{13}{2}
\][/tex]
Next, calculate the y-coordinate of the midpoint:
[tex]\[
y_{\text{midpoint}} = \frac{1 + 5}{2} = 3
\][/tex]
Therefore, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[
\left( \frac{13}{2}, 3 \right)
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\left( \frac{13}{2}, 3 \right)}
\][/tex]
