To find the midpoint $M$ of a line segment with endpoints $P(x_1, y_1)$ and $Q(x_2, y_2)$, you can use the midpoint formula:

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

Given the endpoints $P(3, 13)$ and $Q(10, 8)$, you can substitute these coordinates into the formula:

$M = \left( \frac{3 + 10}{2}, \frac{13 + 8}{2} \right)$

Let's calculate it:

$M = \left( \frac{13}{2}, \frac{21}{2} \right)$

Simplifying, the coordinates of the midpoint $M$ are:

$M = \left( 6.5, 10.5 \right)$

So, the midpoint $M$ is $(6.5, 10.5)$.

Would you like more details on how this was calculated, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How would the midpoint formula change if the line segment was in 3D space?
2. What is the significance of the midpoint in geometry?
3. How can you find the length of the line segment given its endpoints?
4. If the midpoint is given, how can you determine one endpoint if the other is known?
5. What are the properties of the midpoint in coordinate geometry?

Tip: The midpoint divides the line segment into two equal parts and is useful in finding the center of a line segment or for bisecting it.