Question

If $z_1,z_2,z_3,z_4$ are the affixes of four points in the Argand plane, $z$ is the affix of a point such that $|z-z_1|=|z-z_2|=|z-z_3|=|z-z_4|$, then the points $z_1,z_2,z_3,z_4$ can lie on which among the following curves

• A. Circle
• B. Rectangle
• C. Square
• D. Triangle

Answer 1

Answer: (A), (B), (C)

The correct options are
A Circle
B Rectangle
C Square

We have,
$|z-z_1|=|z-z_2|=|z-z_3|=|z-z_4|$
Therefore, the point having affix $z$ is equidistant from the four points having affixes $z_1,z_2,z_3,z_4$.
Thus $z$ is either the centre of a circle having $z_1,z_2,z_3,z_4$ on its circumference (or)
Point of intersection of diagonals of a square or rectangle having $z_1,z_2,z_3,z_4$ as its vertices as diagonals gets bisected each other.