Question

Find the centroid of ∆ABC whose vertices are A(−1, 0), B(5, −2) and C(8, 2).

Answer 1

Here, (x₁ = −1, y₁ = 0), (x₂ = 5, y₂ = −2) and (x₃ = 8, y₃ = 2).
Let G(x, y) be the centroid of the ∆ABC. Then,
$$\begin{gathered} x=\frac{1}{3}\left(x_1+x_2+x_3\right)=\frac{1}{3}\left(-1+5+8\right)=\frac{1}{3}\left(12\right)=4 \\ y=\frac{1}{3}\left(y_1+y_2+y_3\right)=\frac{1}{3}\left(0-2+2\right)=\frac{1}{3}\left(0\right)=0 \end{gathered}$$
Hence, the centroid of ∆ABC is G(4, 0).