Two vertices of a triangle are (3 2) (-2 1) and its centroid is (5/3 -1/3) find the third vertex

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Two vertices of a triangle are 3, 5 and 7,4. If its centroid is 2, 1, find the third vertex.

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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)`