A) \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]
B) \[{{z}_{1}}+4{{z}_{2}}+{{z}_{3}}=0\]
C) \[{{z}_{1}}+{{z}_{2}}+4{{z}_{3}}=0\]
D) \[{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]
Correct Answer: D
Solution :
The affix of G is\[\frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3}\]. Since \[z=0\]is the mid point of\[AG\]. Therefore affix of the mid-point of \[AG\] is 0. Þ \[\frac{\frac{{{z}_{1}}+{{z}_{2}}+{{z}_{3}}}{3}+{{z}_{1}}}{1+1}=0\Rightarrow 4{{z}_{1}}+{{z}_{2}}+{{z}_{3}}=0\]
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