Complex Numbers And Quadratic Equations question 317
Question: If the vertices of a quadrilateral be $ A=1+2i, $ $ B=-3+i, $ $ C=-2-3i $ and $ D=2-2i $ , then the quadrilateral is
Options:
A) Parallelogram
B) Rectangle
C) Square
D) Rhombus
Show Answer
Answer:
Correct Answer: C
Solution:
Given the vertices of quadrilateral $ A(1+2i),B(-3+i),C(-2-3i) $ and $ D(2-2i) $ Now, $ AB=\sqrt{16+1}=\sqrt{17},BC=\sqrt{16+1}=\sqrt{17} $ $ CD=\sqrt{16+1}=\sqrt{17},DA=\sqrt{16+1}=\sqrt{17} $ $ AC=\sqrt{9+25}=\sqrt{34},BD=\sqrt{25+9}=\sqrt{34} $ Hence it is a square.
BETA
