If (1,1,1)is the centroid of the triangle with (3,-5,7) and (-1, 7, -6)as the two vertices find the third vertex
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Given : (1,1,1 ) is the centroid of the triangle with (3,-5,7) and (-1, 7, -6) as the two vertices
To find : the third vertex
Solution:
Centroid (x , y , z ) = ( ( x₁ + x₂ + x₃) /3 , (y₁ + y₂ + y₃) /3 , ( z₁ + z₂ + z₃) /3 )
Centroid (x , y , z ) = 1,1,1
A = (3,-5,7)
B = (-1, 7, -6)
C = (Cx , Cy , Cz)
=> 1 = ( 3 - 1 + Cx)/ 3 => Cx = 1
1= ( -5 + 7 + Cy)/3 => Cy = 1
1 = ( 7 - 6 + Cz)/3 => Cz = 2
Hence third vertex is ( 1 , 1 , 2 )
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