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To find the midpoint of a line segment with endpoints \((-4, 4)\) and \((5, -1)\), we use the midpoint formula:

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

Given the points \((-4, 4)\) and \((5, -1)\):

1. Calculate the x-coordinate of the midpoint:
   \[
   \frac{-4 + 5}{2} = \frac{1}{2}
   \]

2. Calculate the y-coordinate of the midpoint:
   \[
   \frac{4 + (-1)}{2} = \frac{3}{2}
   \]

Thus, the midpoint is \(\left( \frac{1}{2}, \frac{3}{2} \right)\).

Looking at the answer choices, the correct one is:
\[
\boxed{\left( \frac{1}{2}, \frac{3}{2} \right)}
\]

Would you like more details or have any questions about this solution?

Here are some related questions:
1. What is the formula for finding the distance between two points?
2. How do you calculate the slope of a line given two points?
3. What are the applications of the midpoint formula in geometry?
4. Can the midpoint formula be used in three-dimensional geometry?
5. How would the midpoint formula change if we were working with parametric equations?

**Tip**: For complex geometry problems, visualizing the points and line segments on a graph can help in understanding the relationships better.

Find the midpoint of the line segment with the given endpoints (-4, 4), (5, -1).

This solution explains how to find the midpoint of a line segment given endpoints (-4, 4) and (5, -1) using the midpoint formula. This problem covers fundamental concepts in coordinate geometry and is suitable for students in Grades 7-9.

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