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Standard XII

Mathematics

Two Point Form of a Line

The points Z ...

Question

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

z₁ + z₂ = z₃ + z₄

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z₁ - z₂ = z₄ - z₃

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z₁ + z₂ + z₃ + z₄ = 0

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none of these

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Solution

The correct option is B
z₁ - z₂ = z₄ - z₃

Consider the above parallelogram. The meeting point of the diagonals is the midpoint of the diagonals.

The diagonals bisect each other.
$\Rightarrow$ $\frac{z_{1} + z_{2}}{2}$ = $\frac{z_{2} + z_{4}}{2}$
$\Rightarrow$ $z_{1}$ - $z_{2}$ = $z_{4}$ - $z_{3}$

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

The correct option is B z1 - z2 = z4 - z3 Consider the above parallelogram. The meeting point of the diagonals is the midpoint of the diagonals. The diagonals bisect each other. ⇒z1+z22 = z2+z42 ⇒ z1 - z2 = z4 - z3

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