Complex Numbers And Quadratic Equations question 325
Question: If $ z_1,z_2,z_3,z_4 $ are the affixes of four points in the Argand plane and $ z $ is the affix of a point such that $ |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| $ , then $ z_1,z_2,z_3,z_4 $ are
Options:
A) Concyclic
B) Vertices of a parallelogram
C) Vertices of a rhombus
D) In a straight line
Show Answer
Answer:
Correct Answer: A
Solution:
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 the affix of either the centre of a circle or the point of intersection of diagonals of a square or rectangle. Therefore $ z_1,z_2,z_3,z_4 $ are either concyclic or vertices of a square. Hence $ z_1,z_2,z_3,z_4 $ are concyclic.
BETA
