Question

If the centroid of △ABC having vertices A(a, b), B(b, c) and C(c, a) is the origin, then find the value of (a + b + c).

Answer 1

The given points are A(a,b), B(b,c) and C(c,a)

Here,

(x₁ = a,y₁ = b),(x₂ = b,y₂ = c) and (x₃ = c,y₃ = a)

Let the centroid be (x,y).

Then,

But it is given that the centroid of the triangle is the origin. 

Then, we have

\(\frac{a\,+\,b\,+\,c}{3}=0\)

\(\Rightarrow\) a + b + c = 0