Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 28

scalene

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: $a=\sqrt{(-1-1)^2+(-6-1)^2}=\sqrt{53}$, $b=\sqrt{(-1-4)^2+(-6-(-5))^2}=\sqrt{26}$, $c=\sqrt{(1-4)^2+(1-(-5))^2}=\sqrt{45}$, thus the triangle is scalene.