To find the midpoint of a line segment with endpoints [tex]\( G(10, 1) \)[/tex] and [tex]\( H(3, 5) \)[/tex], we use the midpoint formula. The midpoint formula is given by:
[tex]\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, [tex]\(G(10, 1)\)[/tex] gives us [tex]\( x_1 = 10 \)[/tex] and [tex]\( y_1 = 1 \)[/tex], and [tex]\( H(3, 5) \)[/tex] gives us [tex]\( x_2 = 3 \)[/tex] and [tex]\( y_2 = 5 \)[/tex].
Plugging these values into the midpoint formula, we get:
[tex]\[
\text{Midpoint} = \left( \frac{10 + 3}{2}, \frac{1 + 5}{2} \right)
\][/tex]
Now, let's calculate each component individually:
1. For the x-coordinate:
[tex]\[
\frac{10 + 3}{2} = \frac{13}{2} = 6.5
\][/tex]
2. For the y-coordinate:
[tex]\[
\frac{1 + 5}{2} = \frac{6}{2} = 3.0
\][/tex]
Thus, the coordinates of the midpoint of [tex]\( \overline{GH} \)[/tex] are:
[tex]\[
\left( 6.5, 3.0 \right)
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\left( \frac{13}{2}, 3 \right)}
\][/tex]
