Question

If \(\mathrm{G}(-2, 1)\) is the centroid of \(\triangle \mathrm{ABC}\), two of whose vertices are \(\mathrm{A}(1, -6)\) and \(\mathrm{B}(-5, 2)\), find the third vertex of the triangle.

Answer 1

Let the third vertex be $$C(a, b)$$.

$$-2 = \frac{1 + (-5) + a}{3}$$

$$\Rightarrow -6 = a - 4$$

$$\Rightarrow a = -2$$

$$1 = \frac{-6 + 2 + b}{3}$$

$$\Rightarrow 3 = b - 4$$

$$\Rightarrow b = 7$$

Hence the third vertex is $$C(-2, 7)$$.