(Q12) Let A(4,2) , B(6,5) and C(1,4) be the vertices of △ABC.

ABCDEFP

The points (2,3) (x,y) (3,-2) are the vertices of a triangle.If the centroid of this triangle is origin then find(x,y).

Given vertices of triangle are (2,3) (x,y) (3, -2)

Now formula of centroid =
x1+x2+x3
3
 ,
y1+y2+y3
3
Centroid of given triangle = (
+x+
3
 ,
+y-
3
 ) = (
+x
3
 ,
+y
3
 )

But given centroid = origin

(
+x
3
 ,
+y
3
 ) = (0,0)
+x
3
 = 0 and
+y
3
 = 0

+ x = 0 and + y = 0

x = - and y = -

(x,y) = (-, -)