The formula of a midpoint:
[tex]M_{ST}\left(\dfrac{x_S+x_T}{2},\ \dfrac{y_S+y_T}{2}\right)[/tex]
We have:
[tex]M(5,\ -8)\to x_M=5,\ y_M=-8\\T(4,\ -6)\to x_T=4,\ y_T=-6[/tex]
Substitute:
[tex]\dfrac{x_S+4}{2}=5\qquad|\cdot2\\\\x_S+4=10\qquad|-4\\\\x_S=6\\\\\dfrac{y_S+(-6)}{2}=-8\qquad|\cdot2\\\\y_S-6=-16\qquad|+6\\\\y_S=-10[/tex]
Answer: (6, -10)
