Question

Two vertices of a triangle have coordinates (−8, 7) and (9, 4) . If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

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 (−8, 7) and (9, 4)

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 - 8  + 9)/3 , (y + 7 + 4) /3)`

Compare individual terms on both the sides-

`(x + 1 ) / 3 = 0`

So,

 x= - 1

Similarly,

`(y + 11 ) / 3  = 0`

So,

y = - 11

So the co-ordinate of third vertex ( -1 , - 11 )