What represents a characteristic of perpendicular lines in geometry?

Perpendicular lines in geometry are defined by their slopes. 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 ), the other line will have a slope of ( -\frac{1}{m} ). This relationship ensures that the two lines intersect at a right angle, which is the fundamental property of perpendicularity.

For example, if one line has a slope of 2, then the line that is perpendicular to it would have a slope of (-\frac{1}{2}). This negative reciprocal relationship is crucial in determining whether two lines are perpendicular when looking at their equations in slope-intercept form.

Other characteristics mentioned, such as having the same slopes or always being horizontal, do not accurately describe perpendicular lines. Instead, these lines can be at various angles and are not constrained to being horizontal; they can intersect at any angle of 90 degrees. Additionally, the assertion that they can never intersect contradicts the very definition of perpendicular lines, as they are defined precisely by their intersection at right angles. This characteristic makes the negative reciprocal relationship the correct trait of perpendicular lines in geometry.