the perpendicular is the perpendicular bisector.

a straight line that passes through the midpoint of a line segment and is perpendicular to the line segment is called the perpendicular bisector of the line segment (english: perpendicular bisector).

perpendicular bisectors, referred to as "perpendiculars", are a very important part of geometry in junior high schools. use a straight line to divide a line segment into two equal segments from the middle and perpendicular to the divided line segments. this straight line is called the perpendicular bisector of the segment. usually a compass and a ruler are used to draw the drawing.

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

then the equation of the perpendicular bisector can be obtained by assuming that the distance from any point on the line to both endpoints is equal:

(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