To find the midpoint of a line segment with given endpoints, you can use the midpoint formula:

$\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Given the endpoints $(8, 0)$ and $(-2, 4)$, let's substitute the values into the formula:

$\text{Midpoint} = \left( \frac{8 + (-2)}{2}, \frac{0 + 4}{2} \right)$

Simplify each coordinate:

$\text{Midpoint} = \left( \frac{6}{2}, \frac{4}{2} \right) = (3, 2)$

So, the midpoint of the segment is $\boxed{(3, 2)}$.

Would you like more details on this calculation or have any further questions?

Here are some related questions:

1. How would you find the length of the segment with these endpoints?
2. What is the distance from the midpoint to one of the endpoints?
3. Can you find the slope of the line passing through these endpoints?
4. How would the midpoint change if both coordinates of one endpoint were doubled?
5. What if the endpoints were $(8, 0)$ and $(2, -4)$? What would the midpoint be?

Tip: The midpoint formula is essentially the average of the x-coordinates and y-coordinates of the endpoints.