Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 25

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: $a=\sqrt{(-2-1)^2+(5-(-1))^2}=\sqrt{45}$, $b=\sqrt{(-2-4)^2+(5-6)^2}=\sqrt{37}$, $c=\sqrt{(1-4)^2+(-1-6)^2}=\sqrt{58}$, thus the triangle is scalene.