Perpendicularly

Perpendicularly describes the relationship of being at a right angle to something else. In geometry, the term is used to indicate that two lines, planes, or directions meet or are oriented at 90 degrees to each other. The standard symbol for perpendicularity is the right angle sign, often written as ⟂, as in a line AB perpendicular to a line CD (AB ⟂ CD).

Basic properties include that perpendicular lines intersect and form four right angles. A line can also be perpendicular to a plane if it intersects that plane and makes a right angle with every line in the plane that passes through the point of intersection. A segment’s perpendicular bisector is a line or plane perpendicular to the segment at its midpoint, and it is the locus of points equidistant from the segment’s endpoints.

In coordinate geometry, perpendicularity has practical tests. In the plane, lines with slopes m1 and m2 are perpendicular if m1·m2 = -1 (provided neither is vertical). In vector terms, two direction vectors are perpendicular if their dot product is zero.

Perpendicular distance is the shortest distance between a point and a line or between a line and a plane, measured along a line that is perpendicular to the object. The concept is foundational in constructions, surveying, engineering, and graphics, where right angles ensure accuracy and stability.

Usage of perpendicularly appears in phrases such as a line rising perpendicularly to the ground. The term underpins many geometric criteria, from basic angle measurement to more advanced spatial reasoning.