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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.
asked Jan 11, 2013 in GEOMETRY by angel12 Scholar

1 Answer

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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
answered Jan 11, 2013 by richardson Scholar

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