What defines perpendicular lines in relation to their slopes?

Perpendicular lines are defined by their slopes in a specific way. When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other line. This means that if one line has a slope of ( m ), then the slope of the line perpendicular to it would be ( -\frac{1}{m} ).

For example, if one line has a slope of 2, its negative reciprocal would be -1/2. When you multiply these two slopes together (2 and -1/2), the result is -1, demonstrating that they are indeed perpendicular because of how they intersect at right angles.

This relationship is crucial in geometry, especially in coordinate geometry, to understand how angles and orientations work in a plane. The concept of negative reciprocals ensures that when plotted on a graph, the two lines intersect at 90 degrees.

Other potential relationships described, such as slopes being equal or simply not relating to each other, do not apply when defining the characteristic of perpendicular lines.