To determine the midpoint of a line segment between two points, we can use the midpoint formula:

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

Given the points $(-2, -8)$ and $(2, -1)$, we can apply the formula:

• $x_1 = -2$, $x_2 = 2$
• $y_1 = -8$, $y_2 = -1$

Now, let's calculate the midpoint step by step:

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

$M_y = \frac{-8 + (-1)}{2} = \frac{-8 - 1}{2} = \frac{-9}{2} = -4.5$

Thus, the midpoint is:

$M = (0, -4.5)$

The midpoint of the line segment joining the points $(-2, -8)$ and $(2, -1)$ is $(0, -4.5)$.

Would you like more details or have any questions about this? Here are 5 related questions you can explore:

1. What is the distance between these two points?
2. How would the midpoint formula change in 3D space?
3. Can you find the slope of the line segment joining these points?
4. What is the equation of the line passing through these two points?
5. How does the midpoint relate to dividing a segment in different ratios?

Tip: The midpoint is always the average of the coordinates of the two endpoints, making it the "center" of the line segment.