Complex Numbers And Quadratic Equations question 324
Question: The vertices $ B $ and $ D $ of a parallelogram are $ 1-2i $ and $ 4+2i $ , If the diagonals are at right angles and $ AC=2BD $ , the complex number representing $ A $ is
Options:
A) $ \frac{5}{2} $
B) $ 3i-\frac{3}{2} $
C) $ 3i-4 $
D) $ 3i+4 $
Show Answer
Answer:
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 $ ( \frac{5}{2},0 ) $ . Since the diagonals of a parallelogram bisect each other, therefore, the affix of the point of intersection of the diagonals is $ ( \frac{5}{2},0 ) $ . We have $ |\overrightarrow{AE}|=5 $ $ ( \because BD=\frac{1}{2}AC $ and $ AE=AC $, so $ BD=\frac{1}{2}AE $ ) $ Which is satisfied by option .
BETA
