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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?

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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.

Find the midpoint of the line segment with the endpoints A(2,10) and B(8,6).

Learn how to find the midpoint of a line segment given the endpoints A(2,10) and B(8,6). This problem introduces the midpoint formula and demonstrates how to calculate the midpoint step by step. Suitable for students in Grades 6-8.

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