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 ${\displaystyle (x_1,y_1),(x_2,y_2),(x_3,y_3)}$  is-

${\displaystyle (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})}$

So,

${\displaystyle (0,0)=(\frac{x-8 +9}{3},\frac{y+7+4}{3})}$

Compare individual terms on both the sides-

${\displaystyle \frac{x+1}{3}=0}$

So,

 x= - 1

Similarly,

${\displaystyle \frac{y+11}{3} =0}$

So,

y = - 11

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