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

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

In this case, the endpoints are \((9, 5)\) and \((1, 1)\).

1. Calculate the x-coordinate of the midpoint:
   \[
   \frac{9 + 1}{2} = \frac{10}{2} = 5
   \]

2. Calculate the y-coordinate of the midpoint:
   \[
   \frac{5 + 1}{2} = \frac{6}{2} = 3
   \]

Thus, the midpoint is:

\[
(5, 3)
\]

Would you like more details or have any questions?

Here are some related questions:
1. How can the midpoint formula be used to verify the center of a line segment?
2. What are other applications of the midpoint formula in geometry?
3. How is the midpoint concept used in coordinate geometry problems involving triangles?
4. How can finding a midpoint help in dividing a line segment into equal parts?
5. What would happen to the midpoint if both endpoints are translated by the same vector?

**Tip:** The midpoint is always equidistant from both endpoints, which can be helpful in dividing segments symmetrically.

Find the midpoint of the segment with the following endpoints: (9, 5) and (1, 1).

Learn how to find the midpoint of a line segment with endpoints (9, 5) and (1, 1) using the midpoint formula. This problem covers essential concepts in coordinate geometry, ideal for students in Grades 6-8.

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