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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?
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Solution
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
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