The plumb line is the perpendicular bisector.

The perpendicular bisector of a line segment passing through its midpoint and perpendicular to it is called the perpendicular bisector of the segment

The perpendicular bisector, also known as the "vertical bisector", is a very important part of middle school geometry. Using a straight line to divide a line segment into two equal segments from the middle, and perpendicular to the segmented segments, this line is called the perpendicular bisector of this segment. Usually, it is necessary to use a compass and ruler to make the drawing.

Let the coordinates of the two endpoints of the line segment be (x1, y1), (x2, y2)

The equation for the perpendicular bisector can be obtained by the equal distance between any point on the line and its two endpoints：

(x-x1)^2+(y-y1)^2=(x-x2)^2+(y-y2)^2

2(x1-x2)x+2(y1-y2)y=x1^2+y1^2-x2^2-y2^2