Question 209329: Which three points form the vertices of a right triangle?
(A) (0,-2), (1,-2), (5,1)
(B) (1,0), (-2,4) , (4,1)
(C) (-1,-1), (2,-1), (-2,4)
(D) (-1,4), (2,1), (4,3)
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Which three points form the vertices of a right triangle?
(A) p(0,-2), q(1,-2), r(5,1)
pq = 1
pr = sqrt(5^2 + 3^2) = sqrt(34)
qr = sqrt(4^2 + 3^2) = 5
pr^2 <> pq^2 + qr^2
Not a right triangle.
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(B) p(1,0), q(-2,4), r(4,1)
pq = sqrt(3^2 + 4^2) = 5
pr = sqrt(5^2 + 1) = sqrt(26)
qr = sqrt(6^2 + 3^2) = sqrt(45)
Not a right triangle
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(C) p(-1,-1), q(2,-1), r(-2,4)
pq^2 = 3^2 + 2^2 = 13
pr^2 = 1 + 5^2 = 26
qr^2 = 4^2 + 5^2 = 41
Not a right triangle
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(D) p(-1,4), q(2,1), r(4,3)
pq^2 = 3^2 + 3^2 + 18
pr^2 = 5^2 + 1 = 26
qr^2 = 2^2 + 2^2 = 8
pr^2 = pq^2 + qr^2 --> right triangle
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