What is the slope of perpendicular lines?

The slope of perpendicular lines is defined as the negative reciprocal of each other. This means that if one line has a slope of m, the slope of a line that is perpendicular to it would be -1/m. This relationship holds true because the product of the slopes of two perpendicular lines is -1.

For example, if one line has a slope of 2 (which can be represented as a fraction 2/1), the slope of a line perpendicular to it would be the negative reciprocal, which is -1/2. This can be visualized graphically; when two lines are perpendicular, they intersect at right angles, demonstrating that their slopes combine to produce a negative value when multiplied.

Understanding this concept is key in geometry and algebra, as it applies to various problems involving line equations, coordinate systems, and geometric constructions. Recognizing the negative reciprocal relationship helps in determining the slopes of lines that intersect at right angles, which is critical in both analytical and graphical interpretations.