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Two vertices of a triangle are ( 2, -6 ,4) , (4, -2, 3) and its centroid is (8/2 , -1 , 3) , find the third vertex.

 denote centroid as C and vertices as A,B,D

then C(x)= ( A(x)+B(x)+D(x) )/3

substitute for x coordinates of A,B and centroid to find D(x);

similarly find y,z,coordinate of vertex D........

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denote vertices as -a,b, and d;

centroid as c;

then----

c(x)=( a(x)+b(x)+d(x) )/3;

subst. and find x-coordinate of d;

simlarly find d(Y) and d(z).......

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 Centroid (C) = ( 82 , -1 , 3 )

Two vertices of a triangle are A(2,-6,4) and B(4,-2,3) .

Let , third vertices of triangle is ( x,y,z

Third vertices of x =( x+2+4)/3 = 8/2

                               => 2x+4+8 = 24

                               => 2x = 24 - 12

                               => x = 6

Third vertices of y =( -2-6+y)/3 = -1

                               =>  y = 5

Third vertices of z = (4+3+z)/3 = 3

                               => z = 2 

Third vertices of a triangle = (6,5,2)

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