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Standard XII

Mathematics

Two Point Form of a Line

The points Z ...

Question

The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plane are the vertices of a parallelogram taken in order, if and only if

z₁+z₄=z₂+z₃

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z₁+z₃=z₂+z₄

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z₁+z₂=z₃+z₄

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None of these

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Solution

The correct option is B
z₁+z₃=z₂+z₄

Diagonals of a parallelogram ABCDare bisected each other at a point

i.e., $\frac{z_{1} + z_{3}}{2}$ = $\frac{z_{2} + z_{4}}{2}$ $\Rightarrow$ $z_{1}$ + $z_{3}$ = $z_{2}$ + $z_{4}$

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The points z1,z2,z3,z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

The correct option is B z1+z3=z2+z4 Diagonals of a parallelogram ABCDare bisected each other at a point i.e., z1+z32=z2+z42 ⇒ z1+z3=z2+z4

The points $z_{1}, z_{2}, z_{3}, z_{4}$ in the complex plane are the vertices of a parallelogram taken in order, if and only if

The correct option is B
z₁+z₃=z₂+z₄

Diagonals of a parallelogram ABCDare bisected each other at a point

i.e., $\frac{z_{1} + z_{3}}{2}$ = $\frac{z_{2} + z_{4}}{2}$ $\Rightarrow$ $z_{1}$ + $z_{3}$ = $z_{2}$ + $z_{4}$