Slopes of Perpendicular Lines
Perpendicular lines intersect at a right angle.
If two nonvertical lines are perpendicular, then their slopes are negative
reciprocals of each other.
That is, if the slope of one line is
, then the slope of any perpendicular
line is
.
The product of the slopes of two
perpendicular lines is 1. 

Note: To find the negative reciprocal of a
fraction, switch the numerator and the
denominator and change the sign.
For example, the negative reciprocal of
is
. The negative reciprocal of
3 is
.
Example 1
Find the slope of a line perpendicular to the line that passes through the
points (4, 1) and (1, 2).
Solution
First, find the slope of the line through the given points.
Let (x_{1}, y_{1}) = (4, 1) and (x_{2}, y_{2})
= (1, 2). 
m 

Substitute the values in the slope formula.



Simplify. 


The slope of the line through
(4, 1) and (1, 2) is
.
The negative reciprocal of
is
.
A line perpendicular to the line through (4, 1) and (1, 2) has slope
.
Example 2
Determine if line A is perpendicular to line B.
Solution
The slopes,
and
, are not negative reciprocals so the lines are
not perpendicular.
Be careful! The lines do look
perpendicular. But the relationship
between their slopes tells us the lines are
not perpendicular.
