The plane `2x+3y+4z=1` meets the coordinate axis in A, B, C. The centroid of the `DeltaABC` is

Options

A. (2, 3, 4)
B. `((1)/(2), (1)/(3), (1)/(4))`
C. `((1)/(6), (1)/(9), (1)/(12))`
D. `((3)/(2),(3)/(3), (3)/(4))`

Answer

C

Explanation

Given equation can be rewritten as
`(x)/((1)/(2))+(y)/((1)/(3))+(z)/((1)/(4))=1`
`:.` The coordinates of `DeltaABC` is
`A((1)/(2),0,0),B(0,(1)/(3),0),C(0,0,(1)/(4))`
Centroid of triangle
`=(((1)/(2)+0+0)/(3),(0+(1)/(3)+0)/(3),(0+0+(1)/(4))/(3))`
`=((1)/(6),(1)/(9),(1)/(12))`