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To find the midpoint \( M \) of a line segment with endpoints \( T(x_1, y_1) \) and \( U(x_2, y_2) \), we use the midpoint formula:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Given the coordinates:
- \( T(10, 1) \)
- \( U(0, 5) \)

Let's apply the formula:

\[
M_x = \frac{10 + 0}{2} = \frac{10}{2} = 5
\]
\[
M_y = \frac{1 + 5}{2} = \frac{6}{2} = 3
\]

Thus, the coordinates of the midpoint \( M \) are \( (5, 3) \).

Let me know if you'd like further details or have any questions.

Here are 5 related questions you might want to explore:
1. How can you use the distance formula to find the length of the line segment?
2. What happens if one endpoint is moved, how does the midpoint change?
3. Can you find the slope of the line segment given the coordinates of the endpoints?
4. What is the equation of the line passing through the points \( T \) and \( U \)?
5. How would you find the midpoint if one or both of the coordinates were negative?

**Tip:** The midpoint formula can be used in geometry to find the center of a line segment, and it applies in both two-dimensional and three-dimensional space.

A line segment has the endpoints T(10, 1) and U(0, 5). Find the coordinates of its midpoint M.

Learn how to find the midpoint of a line segment with endpoints T(10, 1) and U(0, 5). This problem explores the midpoint formula in geometry, which calculates the center point between two coordinates. Suitable for students in Grades 7-9.

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