A line segment has a midpoint of $(5,\frac{5}{2})$. If one endpoint is $(4,2)$, what is the other endpoint?

Step 1 ：We are given that the midpoint of a line segment is $(5,\frac{5}{2})$ and one endpoint is $(4,2)$.

Step 2 ：The midpoint of a line segment is the average of the x-coordinates and the y-coordinates of the endpoints. Therefore, if we know the midpoint and one endpoint, we can find the other endpoint by using the formula for the midpoint and solving for the unknown endpoint.

Step 3 ：Let's denote the unknown endpoint as $(x,y)$.

Step 4 ：Using the formula for the midpoint, we have $\frac{4+x}{2}=5$ for the x-coordinates and $\frac{2+y}{2}=\frac{5}{2}$ for the y-coordinates.

Step 5 ：Solving the first equation for x, we get $x=6$.

Step 6 ：Solving the second equation for y, we get $y=3$.

Step 7 ：Therefore, the other endpoint of the line segment is $\boxed{{\displaystyle (6,3)}}$.