[tex]\text{The formula of the midpoint of segment AB:}\\\\M(x,\ y)=\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right).\\\\\text{We have the midpoint}\ M(8,\ 2)\ \text{and the endpoint}\ P(5,\ 6).\\\\\text{Substitute:}\\\\\dfrac{5+x}{2}=8\qquad\text{multiply both sides by 2}\\\\5+x=16\qquad\text{subtract 5 from both sides}\\\\\boxed{x=11}\\\\\dfrac{6+y}{2}=2\qquad\text{multiply both sides by 2}\\\\6+y=4\qquad\text{subtract 6 from both sides}\\\\\boxed{y=-2}\\\\Answer:\ \boxed{(11,\ -2)}[/tex]
