To find the midpoint of a line segment whose endpoints are given, we use the midpoint formula. The formula for the midpoint $(M)$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Given endpoints: $\left( 4, 5 \right) \text{ and } \left( 3, 10 \right)$ $\left( 3, -4 \right) \text{ and } \left( -5, -6 \right)$

Plugging in the values:

1. For the first coordinate pair $(4, 5)$ and $(3, 10)$:

$M_x = \frac{4 + 3}{2} = \frac{7}{2} = 3.5$

$M_y = \frac{5 + 10}{2} = \frac{15}{2} = 7.5$

2. For the second coordinate pair $(3, -4)$ and $(-5, -6)$:

$M_x = \frac{3 + (-5)}{2} = \frac{-2}{2} = -1$

$M_y = \frac{-4 + (-6)}{2} = \frac{-10}{2} = -5$

So, the midpoints of the line segments are:

$M = \left(3.5, 7.5 \right) \text{ and } M = \left(-1, -5\right)$

Do you want any details or have any questions?

Here are 5 related questions:

1. How is the midpoint used in geometry?
2. How would you find the midpoint in three-dimensional space?
3. What is the significance of the midpoint in coordinate geometry?
4. Can the midpoint formula be used in real-world applications?
5. How does the distance formula relate to the midpoint formula?

Tip: Always double-check your coordinates when applying the midpoint formula to ensure accuracy!