Lucy should depict in red, in Gauss plane, all complex numbers $z$ that satisfy the condition:
$$|z-1-2\mathrm i|\geq |z+2-5\mathrm i| $$
In which step of her graphical solution did Lucy make a mistake?
Lucy’s solution:
(1) The left side of the equation represents the distance between the number $z$ and the number $1+2 \mathrm{i}$, which Lucy depicted in blue on the figure.
(2) The right side of the equation represents the distance between the number $z$ and the number $-2+5 \mathrm{i}$, which Lucy added to the figure.
(3) Next, Lucy drew a straight line on the figure, containing numbers that are equidistant from the numbers shown in the previous steps.
(4) The solution to the inequality lies within one of the half-planes defined by the boundary line drawn in the previous step. Lucy marked this half-plane in red.
The mistake is in step (1). Here is the corrected image.
The mistake is in step (2). Here is the corrected image.
The mistake is in step (3). Here is the corrected image.
The mistake is in step (4). Here is the corrected image.
