Question

The points $0,2+3i,i,-2-2i$ in the argand plane are the vertices of a

• A. rectangle
• B. rhombus
• C. trapezium
• D. parallelogram

Answer 1

Answer: (D)

Let $A=0$,
$B=2+3i$,
$C=i$,
$D=-2-2i$
Now, $AB=\sqrt{2^2+3^2}=\sqrt{13}$
$BC=\sqrt{2^2+2^2}=\sqrt{8}$
$CD=\sqrt{2^2+3^2}=\sqrt{13}$
$DA=\sqrt{2^2+2^2}=\sqrt{8}$
Diagonals $AC=\sqrt{0+1^2}=1$
and $BD=\sqrt{{\left(4\right)}^2+{\left(5\right)}^2}=\sqrt{41}$ which are not equal.
Hence given vertices are the vertices of a parallelogram.