A(6, y), B(-4, 4) and C(x, -1) are the vertices of ΔABC whose centroid is the origin. Calculate the values of x and y.

By using the centroid formula,

$(x, y) = \Big( \dfrac{x$1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3} \Big)

Origin (0,0) is the centroid of triangle ABC.

Solving for x-coordinate:

$\Rightarrow 0 = \Big(\dfrac{6 + (-4) + x}{3}\Big) \\[1em] \Rightarrow 0 = 2 + x \\[1em] \Rightarrow x = -2.$

Solving for y-coordinate:

$\Rightarrow 0 = \Big(\dfrac{y + 4 + (-1)}{3}\Big) \\[1em] \Rightarrow 0 = y + 3 \\[1em] \Rightarrow y = -3.$

Hence, x = -2 and y = -3.