To find the midpoint of a line segment with endpoints [tex]\( A(6, 10) \)[/tex] and [tex]\( B(4, 8) \)[/tex], we use the midpoint formula. The midpoint [tex]\( M \)[/tex] of the line segment with endpoints [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of point [tex]\( A \)[/tex] are [tex]\( (x_1, y_1) = (6, 10) \)[/tex] and the coordinates of point [tex]\( B \)[/tex] are [tex]\( (x_2, y_2) = (4, 8) \)[/tex]. Substituting these values into the midpoint formula, we get:
[tex]\[
M = \left( \frac{6 + 4}{2}, \frac{10 + 8}{2} \right)
\][/tex]
First, we calculate the x-coordinate of the midpoint:
[tex]\[
\frac{6 + 4}{2} = \frac{10}{2} = 5.0
\][/tex]
Next, we calculate the y-coordinate of the midpoint:
[tex]\[
\frac{10 + 8}{2} = \frac{18}{2} = 9.0
\][/tex]
Therefore, the midpoint [tex]\( M \)[/tex] of the line segment with endpoints [tex]\( A(6, 10) \)[/tex] and [tex]\( B(4, 8) \)[/tex] is:
[tex]\[
M = (5.0, 9.0)
\][/tex]
Thus, the midpoint of the line segment is [tex]\( \boxed{(5.0, 9.0)} \)[/tex].
