The problem asks for the coordinates of the midpoint $M$ of a line segment $AB$, where the endpoints are $A(6, -1)$ and $B(-6, -6)$.

To find the midpoint $M(x_m, y_m)$ of a line segment, we use the midpoint formula:

$x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$

Given:

• $A(6, -1)$
• $B(-6, -6)$

Step 1: Apply the formula to the $x$-coordinates:

$x_m = \frac{6 + (-6)}{2} = \frac{0}{2} = 0$

Step 2: Apply the formula to the $y$-coordinates:

$y_m = \frac{-1 + (-6)}{2} = \frac{-7}{2} = -3.5$

Thus, the coordinates of the midpoint $M$ are: $M(0, -3.5)$

This matches the answer provided in the image.

Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would you find the length of the line segment $AB$?
2. What is the slope of the line passing through points $A$ and $B$?
3. How does the midpoint formula work in three dimensions?
4. How do you find the equation of the line passing through points $A$ and $B$?
5. How would the midpoint change if one of the coordinates was shifted?

Tip: The midpoint formula can be extended to find midpoints in higher dimensions (3D or more) by averaging each corresponding coordinate pair!