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To find the midpoint \( M \) of the line segment \( \overline{AB} \), we use the midpoint formula:

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

Given points:
\( A (6, -2) \) and \( B (-13, -3) \).

Plug in the coordinates:

1. For the x-coordinate:
   \[
   \frac{6 + (-13)}{2} = \frac{-7}{2} = -3.5
   \]

2. For the y-coordinate:
   \[
   \frac{-2 + (-3)}{2} = \frac{-5}{2} = -2.5
   \]

Thus, the midpoint \( M \) is:

\[
M = (-3.5, -2.5)
\]

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

Here are five related questions:
1. How do you find the midpoint if given three-dimensional coordinates?
2. What is the distance formula for finding the length of \( \overline{AB} \)?
3. How can you verify if a point is the midpoint of a segment?
4. How does the midpoint formula change in polar coordinates?
5. How can the midpoint formula be applied in vector geometry?

**Tip:** The midpoint formula is essentially averaging the coordinates of two endpoints to find the center point.

Find the midpoint of the line segment AB where A(6, -2) and B(-13, -3).

Learn how to find the midpoint of the line segment AB with given points A(6, -2) and B(-13, -3) using the midpoint formula. This problem involves fundamental coordinate geometry and is suitable for students in Grades 6-8.

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