Question

Find the third vertex of a triangle, if two of its vertices are at (–3, 1) and (0, –2) and the centroid is at the origin.

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 (−3, 1) and (0, −2)

The co-ordinate of the centroid is (0, 0)

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, `(0,0)=((x+0-0)/3,(y+1-2)/3)` 

Compare individual terms on both the sides- 

`(x-3)/3=0` 

So, x = 3 

Similarly, 

`(y-1)/3=0` 

So, y = 1 

So the co-ordinate of third vertex (3, 1).