The midpoint coordinates are: (8,-2)
We can label this coordinates as follows
[tex]\begin{gathered} x_m=8 \\ y_m=-2 \end{gathered}[/tex]The coordinates for one of the endpoints are: (3,10)
We label this coordinates as follows:
[tex]\begin{gathered} x_1=3 \\ y_1=10_{}_{} \end{gathered}[/tex]We are looking for the other endpoints with the coordinates (x2,y2).
We use the formulas to find the midpoint:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2}_{} \\ y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]But, since we need x2 and y2, we solve for then in the equations:
[tex]\begin{gathered} 2x_m-x_1=x_2_{} \\ 2y_m-y_1=y_2 \end{gathered}[/tex]And we substitute our values into the equations:
For x2:
[tex]\begin{gathered} 2(8)-3=x_2 \\ 16-3=x_2 \\ 13=x_2 \end{gathered}[/tex]For y2:
[tex]\begin{gathered} 2(-2)-10=y_2 \\ -4-10=y_2 \\ -14=y_2 \end{gathered}[/tex]Answer: (13,-14)
