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Question
Let z1,z2,z3,z4 are four points in the Argand plane. If z is 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?
Let z1,z2,z3,z4 are four points in the Argand plane. If z is 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 z is equidistant from the four points z1,z2,z3,z4
If z1,z2,z3,z4 lies on a circle, then z is the centre and it will be equidistant.
If z1,z2,z3,z4 forms a rectangle or square, the point of intersection of diagonals will be z
We have,
|z−z1|=|z−z2|=|z−z3|=|z−z4|
Therefore, the point z is equidistant from the four points z1,z2,z3,z4
If z1,z2,z3,z4 lies on a circle, then z is the centre and it will be equidistant.
If z1,z2,z3,z4 forms a rectangle or square, the point of intersection of diagonals will be z
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