Using the midpoint formula
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]divide the formula for x and y and solve for x2 and y2.
[tex]\begin{gathered} (-6,4)=(\frac{-7+x_2}{2},\frac{11+y_2}{2}) \\ -6=\frac{-7+x_2}{2} \\ 4=\frac{11+y_2}{2} \end{gathered}[/tex]solve for x2
[tex]\begin{gathered} -6=\frac{-7+x_2}{2} \\ -12=-7+x_2 \\ -12+7=x_2 \\ x_2=-5 \end{gathered}[/tex]solve for y2
[tex]\begin{gathered} 4=\frac{11+y_2}{2} \\ 8=11+y_2 \\ 8-11=y_2 \\ y_2=-3 \end{gathered}[/tex]The coordinates of the other endpoint is (-5,-3)