A) \[\frac{5}{2}\]
B) \[3i-\frac{3}{2}\]
C) \[3i-4\]
D) \[3i+4\]
Correct Answer: B
Solution :
We have \[|\overrightarrow{BD}|=|(4+2i)-(1-2i)|=\sqrt{9+16}=5\] Let the affix of A be \[z=x+iy\] The affix of the mid point of BD is \[\left( \frac{5}{2},0 \right)\]. Since the diagonals of a parallelogram bisect each other, therefore, the affix of the point of intersection of the diagonals is \[\left( \frac{5}{2},0 \right)\]. We have \[|\overrightarrow{AE}|=5\] \[\left( \because BD=\frac{1}{2}AC=AE \right)\] Which is satisfied by option .You need to login to perform this action.
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