Question

A(6, y), B(–4, 4) and C(x, –1) are the vertices of \(\triangle \mathrm{ABC}\) whose centroid is the origin. Calculate the values of x and y.

Answer 1

The centroid is the origin $$(0, 0)$$.

So $$\frac{6 + (-4) + x}{3} = 0$$

$$\Rightarrow 2 + x = 0$$

$$\Rightarrow x = -2$$

$$\frac{y + 4 + (-1)}{3} = 0$$

$$\Rightarrow y + 3 = 0$$

$$\Rightarrow y = -3$$

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