Question

What type of triangle is formed by joining the points D(7, 3), E(8, 1), and

Answer 1

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