Perpendicular lines are two lines that intersect at a 90-degree angle (right angle). In coordinate geometry, if one line has slope m, a perpendicular line has slope −1/m (the negative reciprocal). This elegant relationship comes from the fact that perpendicular slopes multiply to give −1: m₁ × m₂ = −1. Perpendicular lines appear everywhere in the physical world: the edges of a square, the axes of a coordinate plane, the walls meeting at a corner of a room, and countless geometric constructions. Understanding perpendicularity is crucial for geometry, engineering, and architecture.

Finding the equation of a perpendicular line requires two pieces of information: the slope of the original line (to compute its negative reciprocal) and a point through which the perpendicular must pass. Using the point-slope form y − y₁ = m(x − x₁), where m is the perpendicular slope and (x₁, y₁) is the given point, you can derive the equation instantly. This relationship makes perpendicular lines powerful tools for construction and design, whether in architecture, mathematics, or engineering applications.