Complex Numbers And Quadratic Equations question 346
Question: If $ z_1,z_2,z_3 $ are affixes of the vertices $ A,B $ and $ C $ respectively of a triangle $ ABC $ having centroid at $ G $ such that $ z=0 $ is the mid point of $ AG, $ then
Options:
A) $ z_1+z_2+z_3=0 $
B) $ z_1+4z_2+z_3=0 $
C) $ z_1+z_2+4z_3=0 $
D) $ z_1+z_2+z_3=0 $
Show Answer
Answer:
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 $ \frac{z}{2} $. Þ $ \frac{\frac{z_1+z_2+z_3}{3}+z_1}{1+1}=0\Rightarrow 4z_1+z_2+z_3=0 $
BETA
