Question

The centroid of the triangle with vertices (1, 4), (2, 8), and (3, 2) is .

• A. $(2,\frac{14}{3})$
• B. $(2,\frac{4}{3})$
• C. $(3,\frac{1}{3})$

Answer 1

The correct option is A $(2,\frac{14}{3})$

Given: Vertices of the triangle are (1, 4), (2, 8), and (3, 2).

We know that centroid of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$.

So,
Centroid = $(\frac{1+2+3}{3},\frac{4+8+2}{3})$
Centroid = $(\frac{6}{3},\frac{14}{3})$
Centroid = $(2,\frac{14}{3})$