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