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Parallel and Perpendicular Lines

Parallel lines are coplanar lines that never intersect.

In two dimensions, parallel lines have the same slope .

Example:

The two lines

y = 3 x + 8 y = 3 x 4

are parallel, since they both have slope 3 .

 

Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get 1 .

Example:

The lines

y = 1 3 x + 2 y = 3 x 4

are perpendicular, since

( 1 3 ) ( 3 ) = 1

Exception : A horizontal line and a vertical line are perpendicular, even though the product of their slopes ( 0 × ) is undefined.