first, we find the length of each side, then:
for TR
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(-8-(-6))^2+(-7-7)^2} \\ d=\sqrt[]{(-8+6)^2+(-14)^2} \\ d=\sqrt[]{(-2)^2+196} \\ d=\sqrt[]{4+196} \\ d=\sqrt[]{100}=10 \end{gathered}[/tex]
answer: TR = 10
for NT
[tex]\begin{gathered} d=\sqrt[]{(-6-5)^2+(7-0)^2} \\ d=\sqrt[]{(-11)^2+7^2} \\ d=\sqrt[]{121+49} \\ d=\sqrt[]{170} \\ d=13.04 \end{gathered}[/tex]
answer: NT = 13.04
for RN
[tex]\begin{gathered} d=\sqrt[]{(5-(-8))^2+(0-(-7))^2} \\ d=\sqrt[]{(5+8)^2+7^2} \\ d=\sqrt[]{13^2+49} \\ d=\sqrt[]{169+49} \\ d=\sqrt[]{218} \\ d=14.76 \end{gathered}[/tex]
answer: RN = 14.76
therefore the sides are:
10
13.04
14.76
so, If all three sides of the triangle are a different length then the triangle is a SCALENE triangle.
answer: RTN is scalene
