mac1105_lecture12_1

# mac1105_lecture12_1 - L12 Parallel and Perpendicular Lines...

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111 L12 Parallel and Perpendicular Lines; Relations; Functions; Operations on Functions Parallel and Perpendicular Lines Two distinct nonvertical lines 1 L and 2 L with the slopes 1 m and 2 m are parallel if and only if their slopes are equal, that is, 12 mm = . Two lines, 1 L and 2 L , neither of which is vertical, are perpendicular if and only if the product of their slopes is 1 , that is, 1 ⋅= or 1 2 1 m m = − , that is, the slopes 1 m and 2 m are negative reciprocals of each other.

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112 Special Cases : 1. Any two vertical lines are parallel. 2. A vertical line is perpendicular to a horizontal line. Example : Find an equation of the line passing through the point (2,3) which is: parallel to 3 x =− perpendicular to 3 x = −
113 Example : Find an equation of the line passing through the point ( 3,5) which is: parallel to 3 6 x y −= perpendicular to 3 6 x y =

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114 Relation A relation is a rule of correspondence between two sets A and B expressed as a set of all ordered pairs ( , ) x y , where x is an element of A and y
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mac1105_lecture12_1 - L12 Parallel and Perpendicular Lines...

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