*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.

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#### 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)`

Concept: Coordinate Geometry

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