The x-coordinate, xm, of the midpoint is calculated as follows:
[tex]x_M=\frac{x_1+x_2}{2}[/tex]where x1 and x2 are the x-coordinates of the endpoints.
In the point M(2, -1), xm = 2. In S(-4, 5), x1 = -4. Substituting this information and solving for x2 (point T), we get:
[tex]\begin{gathered} 2=\frac{-4+x_2}{2} \\ 2\cdot2=-4+x_2 \\ 4+4=x_2_{} \\ 8=x_2 \end{gathered}[/tex]The x-coordinate of point T is 8.
The y-coordinate, ym, of the midpoint is calculated as follows:
[tex]y_M=\frac{y_1+y_2}{2}[/tex]where y1 and y2 are the x-coordinates of the endpoints.
In the point M(2, -1), ym = -1. In S(-4, 5), y1 = 5. Substituting this information and solving for y2 (point T), we get:
[tex]\begin{gathered} -1=\frac{5+y_2}{2} \\ (-1)\cdot2=5+y_2 \\ -2-5=y_2 \\ -7=y_2 \end{gathered}[/tex]The y-coordinate of point T is -7.
Point T has the coordinates (8, -7)
