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)

parallelogram

Answer 2

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.