Find the third vertex of a triangle, if two of its vertices are

We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be.

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

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

So,

$(0,0)=\left(\frac{x+0-3}{3}, \frac{y+1-2}{3}\right)$

Compare individual terms on both the sides-

$\frac{x-3}{3}=0$

So,

$x=3$

Similarly,

$\frac{y-1}{3}=0$

So,

$y=1$

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