Question

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

Answer 1

I didn't understand this question please write this question correctly

Answer 2

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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