The midpoint is given by the following expression:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
Therefore:
[tex](M_x,M_y)=(\frac{X_1+X_2}{2},\frac{y_1+y_2}{2})[/tex]Replacing:
Mx= 5 and My=6
Qx= X1 =-1 and Qy= y1=3
Rx=X2 and Ry= Y2
[tex](5,6)=(\frac{-1+x_2}{2},\frac{3+y_2}{2})[/tex]Equating the x component and solving for X2:
[tex]\begin{gathered} 5=\frac{-1+x_2}{2} \\ 5*2=-1+x_2 \\ 10+1=x_2 \\ x_2=11 \end{gathered}[/tex]Doing the same with the y component:
[tex]\begin{gathered} 6=\frac{3+y_2}{2} \\ 6*2=3+y_2 \\ y_2=12-3=9 \\ y_2=9 \end{gathered}[/tex]Answer: the coordinates of R are: (X2,Y2) = (11 , 9).
