Question

(3,-5), (4,3), (11,-4) Find the centroids of the triangles whose vertices are given

Answer 1

Centroid of triangle whose vertices are (x1,y1);(x2,y2);(X3,y3)=(x1 +x2+X3)/3,(y1+y2+y3)/3
(3+4+11)/3,(-5+3-4)/3
=18/3,-6/3
=(6,-2)
Therefore the centroid of given triangle is (6,-2)

Answer 2

Solution :

Let ( x , y ) is the centroid of a

triangle whose veriticies are

A(3,-5) = ( x1, y1),

B(4,3) = ( x2, y2 ),

C(11,-4) = ( x3, y3 ),

x = ( x1 + x2 + x3 )/3

=> x = ( 3 + 4 + 11 )/3

=> x = 18/3

=> x = 6 ,

y = ( y1 + y2 + y3 )/3

=> y = ( -5 + 3 -4 )/3

=> y = -6/3

=> y = -2

Therefore ,

Centroid ( G ) = ( x , y )

= ( 6 , -2 )

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