Question

If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a³ + b³ + c³ =

(a) abc

(b) 0

(c) a + b + c

(d) 3 abc

Answer 1

The co-ordinates of the vertices are (a, b); (b, c) and (c, a)

The co-ordinate of the centroid is (0, 0)

We know that the co-ordinates of the centroid of a triangle whose vertices are is

So,

Compare individual terms on both the sides-

Therefore,

We have to find the value of -

Now as we know that if,

Then,

So the answer is (d)