The formula of a midpoint of PQ:
[tex]M\left(\dfrac{x_P+x_Q}{2},\ \dfrac{y_P+y_Q}{2}\right)[/tex]
We have M(5, -2) and P(11, -10). Substitute:
[tex]x_M=\dfrac{x_P+x_Q}{2},\ x_M=5,\ x_P=11:\\\\\dfrac{11+x_Q}{2}=5\qquad|\cdot2\\\\11+x_Q=10\qquad|-11\\\\x_Q=-1\\\\y_M=\dfrac{y_P+y_Q}{2},\ y_M=-2,\ y_P=-10\\\\\dfrac{-10+y_Q}{2}=-2\qquad|\cdot2\\\\-10+y_Q=-4\qquad|+10\\\\y_Q=6[/tex]
Answer: Q(-1, 6)
