A line segment has one endpoint at $(6,8)$ and midpoint at $(1,1)$. What is the sum of the coordinates of the other endpoint?
I know that the midpoint of a line segment is the average of the coordinates of the endpoints, so I can use that to find the missing endpoint. If the midpoint is $(1,1)$, then the average of the x-coordinates of the endpoints is $1$, and the average of the y-coordinates of the endpoints is $1$. Let me call the other endpoint $(x,y)$. Then I have the equations: $\frac{x+6}{2} = 1$ and $\frac{y+8}{2} = 1$. Solving for $x$, I get $x+6 = 2$, so $x = -4$. Solving for $y$, I get $y+8 = 2$, so $y = -6$. The other endpoint is $(-4,-6)$. The sum of the coordinates of the other endpoint is $-4 + -6 = -10$. 