The midpoint of the line segment defined by the endpoints $(5, 6)$ and $(9, 10)$ is $(7, 8)$.

To calculate the midpoint of a line segment, we employ the midpoint formula, which is given by:

Here, $(x_1, y_1)$ and $(x_2, y_2)$ represent the coordinates of the two endpoints. In our scenario, the endpoints are $(5, 6)$ and $(9, 10)$.

First, we will determine the x-coordinate of the midpoint. This is accomplished by summing the x-coordinates of the endpoints and dividing the result by 2:

Next, we will compute the y-coordinate of the midpoint by adding the y-coordinates of the endpoints and dividing by 2:

Consequently, the coordinates of the midpoint are $(7, 8)$. This indicates that the point $(7, 8)$ lies precisely halfway between the points $(5, 6)$ and $(9, 10)$ along the line segment. This method can be applied to any pair of endpoints to find the midpoint, making it an invaluable tool in geometry.