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.
Two vertices of ∆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,
$\Rightarrow a=-2, b=7$
Therefore, the third vertex of ∆ABC is C(−2, 7).