To solve for the midpoints of the segments with the given endpoints, we will use the midpoint formula:

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

Let's find the midpoint for each problem:

5. Endpoints: (-8, -10) and (7, 30)

$M = \left( \frac{-8 + 7}{2}, \frac{-10 + 30}{2} \right) = \left( \frac{-1}{2}, \frac{20}{2} \right) = \left( -0.5, 10 \right)$

So, the midpoint is $(-0.5, 10)$.

6. Endpoints: (7, 7) and (7, 3)

$M = \left( \frac{7 + 7}{2}, \frac{7 + 3}{2} \right) = \left( \frac{14}{2}, \frac{10}{2} \right) = \left( 7, 5 \right)$

So, the midpoint is $(7, 5)$.

7. Endpoints: (2.5, -1) and (23.5, 16)

$M = \left( \frac{2.5 + 23.5}{2}, \frac{-1 + 16}{2} \right) = \left( \frac{26}{2}, \frac{15}{2} \right) = \left( 13, 7.5 \right)$

So, the midpoint is $(13, 7.5)$.

Would you like a more detailed explanation of any of these? Let me know if you have questions!

Here are 5 related questions to expand on:

1. How do you find the distance between two points?
2. How does the midpoint relate to dividing a segment into two equal parts?
3. What is the significance of the midpoint in geometry?
4. Can you find the midpoint in three-dimensional space?
5. How would the midpoint formula change if the coordinate system were different?

Tip:

Always double-check your arithmetic when calculating midpoints, especially when working with negative or decimal values!