To find the midpoint of a line segment with endpoints $A(-3, -2)$ and $B(3, 2)$, we use the midpoint formula:

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

where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of points $A$ and $B$ respectively.

For the given points:

• $A(-3, -2)$ means $x_1 = -3$ and $y_1 = -2$
• $B(3, 2)$ means $x_2 = 3$ and $y_2 = 2$

Now, applying the formula:

$M_x = \frac{-3 + 3}{2} = \frac{0}{2} = 0$ $M_y = \frac{-2 + 2}{2} = \frac{0}{2} = 0$

Thus, the midpoint $M$ is at the coordinate $(0, 0)$.

Would you like further details on this solution or have any questions?

Here are some related questions:

1. How would the midpoint change if both endpoints were in different quadrants?
2. What is the significance of the midpoint in geometry?
3. How can you find the distance between the two endpoints?
4. What happens if the coordinates of one point are negative and the other is positive?
5. Can the midpoint ever have fractional coordinates?

Tip: The midpoint formula is especially useful for dividing line segments into equal parts or for finding the center of geometric shapes.