use the midpoint formula to determine the midpoint of the given line segment.

Explanation:

Step1: Identify the endpoints

The endpoints of the line - segment are $(4,2)$ and $(7,8)$.

Step2: Recall the mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step3: Calculate the x - coordinate of the mid - point

$x=\frac{4 + 7}{2}=\frac{11}{2}=5.5$

Step4: Calculate the y - coordinate of the mid - point

$y=\frac{2+8}{2}=\frac{10}{2}=5$

Answer:

$(5.5,5)$