I have another math question that I can't figure out?

Question

 

 

Q: Determine if the measurements of the sides of the Triangle DEF and classify the triangle by its sides. D(1,2) E(5,-2) F(-2,-1)

again please explain how the answer was found.

Answer 1

Given that points D(1,2) E (5,-2) F (-2,-1)

 

Note : Distance formula (x₁, y₁) , (x₂ , y₂)

 

 Than D = √[(x₂ - x₁)^2 + (y₂ - y₁)^2]

 

D = (1 , 2) E = (5 , -2) F = (-2 ,-1)

 

DE = √ [(5-1)^2+(-2-2)^2]

 

Simplify

 

= √[(4)^2+(-4)^2]

 

= √[16+16]

 

=√32

 

EF = √[(-2-5)^2+(-1-(-2))^2]

 

Simplify

 

= √[(-7)^2+(1)^2]

 

= √[49+1]

 

= √50

 

DF = √[(-2-1)^2+(-1-2)^2]

 

Simplify

 

= √[(-3)^2+(-3)^2]

 

= √[9+9]

 

= √18

 

DE^2+DF^2 = EF^2

 

[√32]^2+[√18]^2 = [√50]^2

 

Simplify

 

32+18=50

 

50=50

 

So ,

 

DEF is right triangle