If `z_1, z_2, z_3` be the affixes of the vertices `A, B Mand C` of a triangle having centroid at G such ;that `z = 0` is the mid point of AG then `4z_1 + Z_2 + Z_3 =`

Options

A. `4z_(1)+z_(2)+z_(3)=0`
B. `z_(1)+4z_(1)+z_(3)=0`
C. `z_(1)+z_(2)+4z_(3)=0`
D. `z_(1)+z_(2)+z_(3)=0`

Answer

A

Explanation

We have,
Affix of G `=(z_(1)+z_(2)+z_(3))/(3)`
It is given that z=0, is the mid-point of AG.
`therefore` Affix of the mid-point of AG=0
`rArr =(z_(1)+z_(2)+z_(3))/(2) = 0 rArr (4z_(1)+z_(2)+z_(3))/(2) rArr 0 (4z_(1)+z_(2)+z_(3))/(6) = 0 rArr 4z_(1)+z_(2)+z_(3)=0`