Question

A quadrilateral ABCD has masses of 1, 2, 3 and 4 units located respectively at its vertices A (-1, -2, 2),

B(3, 2, -1), C(1, -2, 4), and D(3, 1, 2). Find the coordinates of the centroid​

Answer 1

Given : quadrilateral ABCD has masses of 1, 2, 3 and 4 units located respectively at its vertices A (-1, -2, 2),  B(3, 2, -1), C(1, -2, 4), and D(3, 1, 2).  

To Find : Centroid

Solution:

A (-1, -2, 2),  B(3, 2, -1), C(1, -2, 4), and D(3, 1, 2).  

masses of 1, 2, 3 and 4 unit

Centroid    ( x , y , z)

x  =  (1(-1) + 2(3) + 3(1) + 4(3) )/(1 + 2 + 3 + 4)

=> x  = ( - 1 + 6 + 3 + 12)/10

=> x =  20/10

=> x =  2

y = (1(-2) + 2(2) + 3(-2) + 4(1) )/(1 + 2 + 3 + 4)

=>y  = ( - 2 + 4 - 6 + 4)/10

=> y = 0/10

=> y = 0

z  =  (1(2) + 2(-1) + 3(4) + 4(2) )/(1 + 2 + 3 + 4)

=> z = ( 2 - 2 + 12 + 8)/10

=> z = 20/10

=>  z = 2

Centroid = ( 2 , 0 , 2)

coordinates of the centroid​  (  2 , 0 , 2)

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