Question

If A(-1, 0), B(5, -2) and C(8, 2) are the vertices of a △ABC then co-ordinates of its centroid are

(A) (12, 0)

(B) (6, 0)

(C) (0, 6)

(D) (4, 0)

Answer 1

Correct option is (D) (4, 0)

Given,

\(A=(-1,0) \)

\(B=(5,-2)\)

\(C=(8,2)\)

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 the \(\triangle A B C\). Then,

\(x =\frac{x_1+x_2+x_3}{3} \)

\(=\frac{-1+5+8}{3}\)

\(=\frac{12}{3}\)

\( =4\)

\(y=\frac{y_1+y_2+y_3}{3} \)

\( =\frac{0+(-2)+2}{3} \)

\(=\frac{0}{3}\)

\(=0\)

Hence, the centroid of \(\triangle A B C\) is \(G(4,0)\).