To find the midpoint of a line segment with endpoints [tex]\( G(x_1, y_1) \)[/tex] and [tex]\( H(x_2, y_2) \)[/tex], we use the midpoint formula, which is given by:
[tex]\[
\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
For the endpoints [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex], let's apply the formula step by step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{10 + 3}{2} = \frac{13}{2} = 6.5
\][/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 of [tex]\( \overline{GH} \)[/tex] are [tex]\( (6.5, 3) \)[/tex].
Based on these calculations, the correct answer is:
C. [tex]\(\left(\frac{13}{2}, 3\right)\)[/tex]
