To find the midpoint of a line segment with endpoints $(-6, -6)$ and $(1, -3)$, we use the midpoint formula:

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

Substituting the given coordinates:

$M = \left(\frac{-6 + 1}{2}, \frac{-6 + (-3)}{2}\right)$

$M = \left(\frac{-5}{2}, \frac{-9}{2}\right)$

So, the midpoint is:

$M = \left(-\frac{5}{2}, -\frac{9}{2}\right)$

This simplifies to:

$M = (-2.5, -4.5)$

Let me know if you'd like further details!

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Here are some related questions:

1. How would you find the length of this line segment?
2. What are the coordinates of a point one-quarter along the segment?
3. Can you derive the slope of the line passing through these points?
4. What would the midpoint be if one point was at the origin?
5. How would the midpoint change if you moved one point to $(-8, -8)$?

Tip: The midpoint is always the average of the coordinates of the endpoints!