What type of triangle is formed by joining the points D(7, 3), E(8, 1), and
F(4, -1)?
1.equilateral triangle
2.isosceles triangle
3.right triangle
4.acute scalene triangle
5.obtuse scalene triangle


D=(7,3)=(xd,yd)→xd=7, yd=3 E=(8,1)=(xe,ye)→xe=8, ye=1 F=(4,-1)=(xf,yf)→xf=4, yf=-1 DE=sqrt[(xe-xd)^2+(ye-yd)^2] DE=sqrt[(8-7)^2+(1-3)^2] DE=sqrt[(1)^2+(-2)^2] DE=sqrt[1+4] DE=sqrt[5] DE=2.236067978 DE=2.236 EF=sqrt[(xf-xe)^2+(yf-ye)^2] EF=sqrt[(4-8)^2+(-1-1)^2] EF=sqrt[(-4)^2+(-2)^2] EF=sqrt[16+4] EF=sqrt[20] EF=sqrt[4*5] EF=sqrt[4]*sqrt[5] EF=2*sqrt[5] EF=2*(2.236067978) EF=4.472135956 EF=4.472 DF=sqrt[(xf-xd)^2+(yf-yd)^2] DF=sqrt[(4-7)^2+(-1-3)^2] DF=sqrt[(-3)^2+(-4)^2] DF=sqrt[9+16] DF=sqrt[25] DF=5 The three sides are differents: DE=2.236 different to EF=4.472 different to DF=5 Then the triangle scalene Longest side is DF=5 DF^2=(5)^2→DF^2=25 DE^2=(sqrt[5])^2→DE^2=5 EF^2=(2*sqrt[5])^2=(2)^2*(sqrt[5])^2=4*5→EF^2=20 Square of the longest side: DF^2=25 Sum of the square of the other sides: DE^2+EF^2=5+20=25 The square of the longest side=25=Sum of the squares of the other sides, then the triangle is a right triangle The triangle is right triangle and it is a scalene triangle Answer: Option 3. right triangle

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