Given this is a one of the endpoints of the segment:
[tex](1,-3)[/tex]You know that the midpoint is:
[tex](2,9)[/tex]By definition, the formula for finding the midpoint of a segment is:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
- The coordinates of the midpoint are:
[tex](x_m,y_m)[/tex]- And the coordinates of the endpoints are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_m=2 \\ y_m=9 \\ \\ x_1=1 \\ y_1=-3 \end{gathered}[/tex]Then, you can set up this equation to find the x-coordinate of the other endpoint:
[tex]2=\frac{1+x_2}{2}[/tex]Solving for:
[tex]x_2[/tex]You get:
[tex](2)(2)=1+x_2[/tex][tex]\begin{gathered} 4-1=x_2 \\ x_2=3 \end{gathered}[/tex]Set up the following equation to find the y-coordinate of the other endpoint:
[tex]9=\frac{-3+y_2}{2}[/tex][tex](9)(2)=-3+y_2[/tex][tex]\begin{gathered} 18+3=y_2 \\ y_2=21 \end{gathered}[/tex]Hence, the answer is:
[tex](3,21)[/tex]