Perpendicular lines passing through a point are at right angles to each other.
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The shortest path is a line perpendicular to the given line that passes through the given point.
A perpendicular to the line which passes through the given point.
A bisector is a line (or line segment) which passes through the midpoint. You can have multiple lines intersect at this one point, and all of them will bisect the original line segment, since they pass through its midpoint. A perpendicular bisector passes through the midpoint, and also is perpendicular to the original line segment, so there will be only one of those.
Perpendicular lines will only share one point: the point of intersection, where the two lines meet.
In Geometry