Question

Find the centroid of ∆ABC whose vertices are A(2, 2), B(−4, −4) and C(5, −8).

Answer 1

The given points are A(2, 2), B(−4, −4) and C(5, −8).
Here, $\left(x_1=2,y_1=2\right),\left(x_2=-4,y_2=-4\right)\text{and}\left(x_3=5,y_3=-8\right)$
Let G(x, y) be the centroid of $∆ABC$. Then,
$$\begin{gathered} x=\frac{1}{3}\left(x_1+x_2+x_3\right) \\ =\frac{1}{3}\left(2-4+5\right) \\ =1 \end{gathered}$$
$$\begin{gathered} y=\frac{1}{3}\left(y_1+y_2+y_3\right) \\ =\frac{1}{3}\left(2-4-8\right) \\ =\frac{-10}{3} \end{gathered}$$
Hence, the centroid of $∆ABC\text{is}G\left(1,\frac{-10}{3}\right)$.