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.

Answer 1

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)`.