How is it determined if two lines are perpendicular?

To determine if two lines are perpendicular, the key characteristic is related to their slopes. When two lines are perpendicular, the product of their slopes is -1. This means that if you have two lines with slopes ( m_1 ) and ( m_2 ), you can determine their perpendicularity by checking if ( m_1 \cdot m_2 = -1 ). This relationship comes from the geometric interpretation of slopes: when you multiply the slopes of two perpendicular lines, the result is negative, indicating that one line slopes upward while the other slopes downward at a ( 90^\circ ) angle to it.

When examining other potential determinants, such as whether their slopes are equal or their sum equals 1, these do not reflect the condition of perpendicularity. Parallel lines, for example, will have equal slopes, while the sum of slopes equaling 1 does not have any geometrical significance regarding perpendicularity. Additionally, while lines that intersect at a right angle do indicate perpendicularity, the condition related to the product of their slopes provides a more direct and calculable way to confirm this relationship mathematically.

Thus, the most definitive and widely applicable way to assert that two lines are perpendicular is through the condition of