Question

If G(-2, 1) is the centroid of a △ABC and two of its vertices are A(1, -6) and B(-5, 2) , find the third vertex of the triangle.

Answer 1

Two vertices of \(\triangle\)ABC are A(1,-6) and B(-5,2). Let the third vertex be C(a, b).

Then the coordinates of its centroid are

But it is given that G(-2,1) is the centroid. Therefore,

Therefore, the third vertex of \(\triangle ABC\) is C(-2,7).