(Q32) Find the coordinate of centroid of the triangle with following vertices.

 (i) (-1,3),(6,-3) and (-3,6) (ii) (6,2),(0,0) and(4,-7) (iii) (1,-1),(0,6) and(-3,0).

Answer

(i) Given ABC in which A(-1,3),B(6,-3) and C(-3,6),

centroid= (
x1+x2+x3
3
 ,
y1+y2+y3
3
)
= (
-++(-)
3
 ,
+(-)+
3
)= (
3
 ,)

(ii) Given the three vertices of a triangle are A(6,2),B(0,0) and C(4,-7),

Centroid(x,y) = (
x1+x2+x3
3
,
y1+y2+y3
3
)
= (
++
3
,
++(-)
3
)
= (
3
,
-
3
)

(iii) Given (1,-1),(0,6) and (-3,0) are the vertices of a triangle

Centroid(x,y) = (
x1+x2+x3
3
,
y1+y2+y3
3
)
= (
++(-)
3
,
-++
3
)
=(
-
3
,
3
)