Two vertices of a triangle have coordinates (−8, 7) and

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 $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ is-

$\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$

So,

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

Compare individual terms on both the sides-

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

So,

$x=-1$

Similarly,

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

So,

$y=-11$

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