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Question
If z1,z2,z3,z4 are the affixes of four points in the Argand plane, z is the affix of a point such that |z−z1|=|z−z2|=|z−z3|=|z−z4|, then the points z1,z2,z3,z4 can lie on which among the following curves
If z1,z2,z3,z4 are the affixes of four points in the Argand plane, z is the affix of a point such that |z−z1|=|z−z2|=|z−z3|=|z−z4|, then the points z1,z2,z3,z4 can lie on which among the following curves
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Solution
The correct option is C Square
We have,
|z−z1|=|z−z2|=|z−z3|=|z−z4|
Therefore, the point having affix z is equidistant from the four points having affixes z1,z2,z3,z4.
Thus z is either the centre of a circle having z1,z2,z3,z4 on its circumference (or)
Point of intersection of diagonals of a square or rectangle having z1,z2,z3,z4 as its vertices as diagonals gets bisected each other.
We have,
|z−z1|=|z−z2|=|z−z3|=|z−z4|
Therefore, the point having affix z is equidistant from the four points having affixes z1,z2,z3,z4.
Thus z is either the centre of a circle having z1,z2,z3,z4 on its circumference (or)
Point of intersection of diagonals of a square or rectangle having z1,z2,z3,z4 as its vertices as diagonals gets bisected each other.
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