Perpendikale

Perpendikale is a geometric term referring to a line, segment, or direction that forms a right angle (90 degrees) with another line, segment, or plane. In Euclidean geometry, two lines are perpendicular when they intersect and enclose a right angle.

In the plane, two non-parallel lines are perpendicular if and only if their slopes satisfy m1 times m2 equals -1. A vertical line is perpendicular to a horizontal line. The concept is closely linked to the idea of distance: the distance from a point to a line is measured along the perpendicular segment from the point to the line, meeting the line at the foot of the perpendicular. Through a given point not on a line, there is a unique line perpendicular to that line; this is called the perpendicular from the point to the line.

Equations provide a practical way to describe perpendicularity. If a line has equation ax + by + c = 0, a line perpendicular to it has direction vector parallel to the line’s normal (a, b). One perpendicular line through a point (x0, y0) can be written as b x - a y + (a y0 - b x0) = 0. In three dimensions, a line is perpendicular to a plane if it is perpendicular to every line in the plane that passes through their intersection point.

Other related concepts include the perpendicular bisector of a segment, which is the locus of points equidistant from the segment’s endpoints and is perpendicular to the segment at its midpoint. Perpendikale has broad use in construction, surveying, computer graphics, and various fields of mathematics.