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Find the centroids of the triangles whos...

Find the centroids of the triangles whose vertices have the
coordinates `(-7,6) (2,-2) ` and (8,5).

Text Solution

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Let `A(-7,6),B(2,-2)` and `C(8,5)`
Suppose the coordinate of point A are `(x_(1),y_(1))`, coordinates of point B are `(x_(2),y_(2))` and coordinates of point `(x_(3),y_(3))`.
`:.x_(1)=-7,y_(1)=6,x_(2)=2,y_(2)=2,x_(3)=8` and `y_(3)=5`
Let `G(x,y)` be the centroid.
By centroid formula
`x=(x_(1)+x_(2)+x_(3))/3, y=(y_(1)+y_(2)+y_(3))/3`
`:.x=(-7+2+8)/3, :.y+(6+(-2)+5)/3`
`:.x=3/3, :.y=9/3`
`:.x=1, :y=3`
The coordinates of the centroid are (1,3).
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