Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 30

isosceles

The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Hence here: $a=\sqrt{(3-6)^2+(5-9)^2}=\sqrt{25}=5$, $b=\sqrt{(3-11)^2+(5-9)^2}=\sqrt{80}$, $c=\sqrt{(6-11)^2+(9-9)^2}=\sqrt{25}=5$, thus the triangle is isosceles.