SOLUTION: ABC has vertices A(–2, 4), B(6, 0), and C(–4, 0). Is ABC a right triangle?

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Question 672315: ABC has vertices A(–2, 4), B(6, 0), and C(–4, 0). Is ABC a right triangle?
Found 2 solutions by sachi, ewatrrr:
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
1st solution
slope AB=(0-4)/(6+2)=-4/8=-1/2
slope BC=0-0/-4-6=0
slope CA=4-0/-2+4=4/2=2
for ABC to be a right triangle slope any two sides should be -1
slope AB*slope CA=-1
so ABC is a right triangle with 2nd solution
|AB|^2=(-2-6)^2+(4-0)^2=80
|BC|^2=(6+4)^2+(0)=100
|CA|^2=(-2+4)^2+(4-0)^2=20
|BC|^2=|AB|^2+|CA|^2
so ABC is a right triangle with ans

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

C(-4,0)

A(-2,4)  m = -4/-2 = 2

B(6,0)

A(-2,4)  m = -4/8 = -1/2

CA is perpendicular to BA, Yes ABC is a right triangle