A (5, x), B(-4, 3) and C (y, -2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.

Centroid of the triangle is given by (G) = $\Big(\dfrac{x$1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big)

Substituting values we get,

$\Rightarrow (0, 0) = \Big[\dfrac{5 + (-4) + y}{3}, \dfrac{x + 3 + (-2)}{3}\Big] \\[1em] \Rightarrow 0 = \dfrac{5 - 4 + y}{3} \text{ and } 0 = \dfrac{x + 3 - 2}{3} \\[1em] \Rightarrow 0 = y + 1 \text{ and } 0 = x + 1 \\[1em] \Rightarrow y = -1 \text{ and } x = -1.$

Hence, x = -1 and y = -1.