Find the equation of the line that bisects a segment at a 90-degree angle.
Input Coordinates
Analysis Results
y = -1.25x + 10.25
Bisector Equation
The line that passes through the midpoint and is perpendicular to the segment.
Midpoint(5.0, 4.0)
Bisector Slope-1.25
What is a Perpendicular Bisector?
A perpendicular bisector is a line that cuts a line segment into two equal parts at a 90-degree angle. Every point on the perpendicular bisector is equidistant from the endpoints of the segment. This property is used in geometry to find circumcenters of triangles.
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Pro Tips
Find the midpoint: (x1+x2)/2, (y1+y2)/2.
Calculate the slope (m) of the original segment.
The perpendicular slope is the negative reciprocal (-1/m).
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Fun Facts
"In any triangle, the three perpendicular bisectors of the sides meet at a single point called the circumcenter."
"Voronoi diagrams, used in geography and computer science, are essentially collections of perpendicular bisectors."
"The perpendicular bisector can be constructed using only a compass and a straightedge."
