Question

find the centroid of the triangle xyz whose vertices are x 3, -5, y -3, 4 and z 9, -2 ​

Answer 1

centroid of the triangle xyz  = ( 3 , - 1) whose vertices are x = (3 , - 5), y = ( - 3 , 4) & z = ( 9 , - 2)

Step-by-step explanation:

x = (3 , - 5)

y = ( - 3 , 4)

z = ( 9 , - 2)

M is Mid point of  y & z =  ( -3 + 9)/2 , (4 - 2)/2

M = 3 , 1

xM is median

Centroid divides median in 2: 1 ratio

=> Centroid =  ( 2 * 3 + 1 * 3) /(2 + 1)  ,  (2* 1  + 1*(-5))/(2 + 1)

= 9/3 , -3/3

= 3 , - 1

centroid of the triangle xyz  = ( 3 , - 1)

Other method:

Centroid  is    (3 - 3 + 9)/3  , ( -5 +4 - 2)/3

= 3 ,  - 1

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Answer 2

Answer: (3,-1)

Step-by-step explanation:

Centroid of the triangle XYZ = X1+Y1+X1 /3 , X2+Y2+Z2 /3

So, 3+(-3)+9 /3 , -5+4+(-2) /3

=> 9/3 , -3/3

=> 3,-1