Which of the following equations can represen | vedclass

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Question

(B) The equation $|z - 1| = |z - 2| = |z - i|$ represents the circumcenter of a triangle formed by the points $z_1 = 1$,$z_2 = 2$,and $z_3 = i$.$(i)$

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$|z - 1| = |z - 2| = |z - i|$

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(B) The equation $|z - 1| = |z - 2| = |z - i|$ represents the circumcenter of a triangle formed by the points $z_1 = 1$,$z_2 = 2$,and $z_3 = i$.$(i)$ $|z - 1| = |z - i|$ represents the perpendicular bisector of the segment joining $1$ and $i$,which is the line $y = x$.(ii) $|z - 1| = |z - 2|$ represents the perpendicular bisector of the segment joining $1$ and $2$,which is the line $x = 1.5$.(iii) $|z - 2| = |z - i|$ represents the perpendicular bisector of the segment joining $2$ and $i$,which is the line $4x - 2y = 3$.The intersection of these three lines is a single point (the circumcenter),but the condition $|z - 1| = |z - 2| = |z - i|$ defines the point equidistant from the vertices of the triangle formed by $1, 2, i$. Thus,it is associated with the geometry of a triangle.

Which of the following equations can represent a triangle in the complex plane?

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