Question

Is TVS scalene, isosceles, or equilateral? The vertices are T(1,1) V(9,2) and S(7,7)

Answer 1

so the triangle looks more or less like the one in the picture below.

let's check how long each side is, TV, VS and ST.


`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ T(\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad V(\stackrel{x_2}{9}~,~\stackrel{y_2}{2})\qquad \qquad % distance value d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ TV=√((9-1)^2+(2-1)^2)\implies TV=√(8^2+1^2)\implies \boxed{TV=√(65)}\\\\ -------------------------------`


`\bf V(\stackrel{x_2}{9}~,~\stackrel{y_2}{2})\qquad S(\stackrel{x_2}{7}~,~\stackrel{y_2}{7})\qquad \qquad VS=√((7-9)^2+(7-2)^2) \\\\\\ VS=√((-2)^2+5^2)\implies\boxed{ VS=√(29)}\\\\ -------------------------------\\\\ S(\stackrel{x_2}{7}~,~\stackrel{y_2}{7})\qquad T(\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad \qquad ST=√((1-7)^2+(1-7)^2) \\\\\\ ST=√((-6)^2+(-6)^2)\implies \boxed{ST=√(72)}`

so, notice, the sides are all of different lengths, thus the triangle is scalene.