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]
Starting with the coordinates of point [tex]\( G \)[/tex], which are [tex]\( (10, 1) \)[/tex], and the coordinates of point [tex]\( H \)[/tex], which are [tex]\( (3, 5) \)[/tex]:
1. Calculate the [tex]\( x \)[/tex]-coordinate of the midpoint.
[tex]\[
\text{Midpoint}_x = \frac{10 + 3}{2} = \frac{13}{2} = 6.5
\][/tex]
2. Calculate the [tex]\( y \)[/tex]-coordinate of the midpoint.
[tex]\[
\text{Midpoint}_y = \frac{1 + 5}{2} = \frac{6}{2} = 3
\][/tex]
Thus, the coordinates of the midpoint are:
[tex]\[
(6.5, 3.0)
\][/tex]
Therefore, the closest answer in the given options is:
C. [tex]\(\left(\frac{13}{2}, 3\right)\)[/tex]
