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Question
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
Solution
We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be(x,y).
The co-ordinates of other two vertices are A (3, 2) and C (−2, 1)
The co-ordinate of the centroid is`(5/3,-1/3)`
We know that the co-ordinates of the centroid of a triangle whose vertices are
`(x_1,y_1),(x_2,y_2),(x_3,y_3)`is
`((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3)`
So, `(5/3,-1/3)=((x+3-2)/3,(y+2+1)/3)`
Compare individual terms on both the sides-
`(x+1)/3=5/3`
So,
x=4
Similarly
`(y+3)/3=-1/3`
So,
y=4
So the co-ordinates of third vertex `(4,-4)`
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