Question

If the centroid of the triangle formed by the points $(a,b),(b,c)$ and $(c,a)$ is at the origin, then $a^3+b^3+c^3$ is equal to

• A. $abc$
• B. $a+b+c$
• C. $3abc$
• D. $0$

Answer 1

The correct option is C $3abc$

Centroid of a triangle is calculated by the formula $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

So, centroid $=(\frac{a+b+c}{3},\frac{b+c+a}{3})=(0,0)$
$=>a+b+c=0$
When $a+b+c=0;a^3+b^3+c^3=3abc$