To find the midpoint of a line segment given two endpoints $A(x_1, y_1)$ and $B(x_2, y_2)$, we can use the midpoint formula:

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

In the image, the coordinates of points $A$ and $B$ are:

• $A(2, 10)$
• $B(8, 6)$

Let's apply the midpoint formula.

$\text{Midpoint} = \left( \frac{2 + 8}{2}, \frac{10 + 6}{2} \right) = \left( \frac{10}{2}, \frac{16}{2} \right) = (5, 8)$

Thus, the midpoint of the line segment is $(5, 8)$.

Would you like a further breakdown of the steps or have any other questions?

Here are 5 related questions for you:

1. How do you calculate the distance between two points using the distance formula?
2. What is the geometric significance of the midpoint in a coordinate plane?
3. Can the midpoint formula be extended to three dimensions? How?
4. How would you find the equation of a line passing through two points?
5. What happens to the midpoint if one of the points is shifted along an axis?

Tip: The midpoint of a segment is always the average of the coordinates of its endpoints, so think of it as a balance point between two locations.