Question

If A(−1, 0), B(5, −2) and C(8, 2) are the vertices of a ∆ABC, then its centroid is

(a) (12, 0)
(b) (6, 0)
(c) (0, 6)
(d) (4, 0)

Answer 1

(d) (4, 0)
The given points are $A\left(-1,0\right),B\left(5,-2\right)\text{and}C\left(8,2\right)$.
Here, $\left(x_1=-1,y_1=0\right),\left(x_2=5,y_2=-2\right)\text{and}\left(x_3=8,y_3=2\right)$
Let G(x, y) be the centroid of $∆ABC$. Then,
$$\begin{gathered} x=\frac{1}{3}\left(x_1+x_2+x_3\right) \\ =\frac{1}{3}\left(-1+5+8\right) \\ =4 \end{gathered}$$
and
$$\begin{gathered} y=\frac{1}{3}\left(y_1+y_2+y_3\right) \\ =\frac{1}{3}\left(0-2+2\right) \\ =0 \end{gathered}$$
Hence, the centroid of $∆ABC$ is G(4, 0).