Chapter 9 Quadratic Relations and Conic Sections - 9.1 Apply the Distance and Midpoint Formulas - 9.1 Exercises - Skill Practice - Page 617: 26

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: $a=\sqrt{(1-4)^2+(4-1)^2}=\sqrt{18}$, $b=\sqrt{(1-7)^2+(4-4)^2}=\sqrt{36}=6$, $c=\sqrt{(4-7)^2+(1-4)^2}=\sqrt{18}$, thus the triangle is isosceles.