Question

A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates $\left(\frac{5}{3},-\frac{1}{3}\right)$. Find the coordinates of the third vertex C of the triangle.

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.

The co-ordinates of other two vertices are A (3, 2) and C (−2, 1)

The co-ordinate of the centroid is

We know that the co-ordinates of the centroid of a triangle whose vertices are is-

So,

Compare individual terms on both the sides-

So,

Similarly,

So,

So the co-ordinate of third vertex