We have a line with two points, a conchoidal point, an endpoint and the midpoint.
Point A will be (-5,8) and the unknown endpoint which we will call B will be (x,y).
The midpoint of AB is (4,3), to find point B, We need to use our generalized midpoint formula:
[tex]\begin{gathered} MP=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \end{gathered}[/tex]Now, we can replace the known values
[tex]MP=(\frac{-5+x}{2},\frac{8+y}{2})[/tex]Solve each separately:
[tex]\begin{gathered} \frac{-5+x}{2}=4 \\ x-5=4\cdot2 \\ x=8+5 \\ x=13 \end{gathered}[/tex][tex]\begin{gathered} \frac{8+y}{2}=3 \\ y+8=3\cdot2 \\ y=6-8 \\ y=-2 \end{gathered}[/tex]In conclusion, the ordered pair for the other endpoint of the line segment is:
[tex](13,-2)[/tex]