Correct answer is (c) (-4,-15)
Two vertices of \(\triangle ABC\) are A(-1,4) and B(5,2).
Let the third vertex be C(a,b).
Then, the coordinates of its centroid are
But it is given that the centroid is G(0,-3).
Therefore,
\(\frac{4\,+\,a}{3}=0\) and \(\frac{6\,+\,b}{3}=-3\)
\(\Rightarrow\) 4 + a = 0 and 6 + b = -9
\(\Rightarrow\) a = -4 and b = -15
Hence, the third vertex of \(\triangle ABC\) is C(-4,-15).
