Parallel and Perpendicular Lines

Two lines are parallel if one can be translated, without rotation, to lie on top of the other. Two lines are perpendicular if they meet at a right angle (an angle of 90°).

Mathematically, the determination of whether two lines are parallel to each other, perpendicular to each other, or neither is based on their slopes.

Consider two lines,  and , in a plane, with slopes  and , respectively.

The lines  and  are parallel if they have the same slope: .

The lines  and  are perpendicular if their slopes are negative reciprocals of each other: .