Question

If the centroid of the triangle formed by points P (a, b), Q(b, c) and R (c, a) is at the origin, what is the value of a + b + c?

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 `(x_1 , y_1 ) ,(x_2 , y_2 ) , (x_3 , y_ 3)`  is-

`((x_1 + x_2 + x_3 ) / 3,(y_1 + y_2 + y_3 ) /3)`

So,

( 0 , 0) = `((a + b+ c ) /3 , ( b+ c+ a ) / 3)`

Compare individual terms on both the sides-

`(a + b+ c) / 3 = 0`

Therefore,

 a + b+ c = 0