To determine the midpoint of the line segment \(\overline{GH}\) with endpoints \(G(10,1)\) and \(H(3,5)\), we use the midpoint formula. The midpoint formula is:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, \((x_1, y_1) = (10, 1)\) and \((x_2, y_2) = (3, 5)\).
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{10 + 3}{2} = \frac{13}{2}
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3
\][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[
\left( \frac{13}{2}, 3 \right)
\][/tex]
So, the correct answer is:
C. [tex]\(\left( \frac{13}{2}, 3 \right)\)[/tex]
