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
|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
. The negative reciprocal of
Find the slope of a line perpendicular to the line that passes through the
points (-4, 1) and (1, -2).
First, find the slope of the line through the given points.
|Let (x1, y1) = (-4, 1) and (x2, y2)
= (1, 2).
|Substitute the values in the slope formula.
The slope of the line through
(-4, 1) and (1, -2) is
The negative reciprocal of
A line perpendicular to the line through (-4, 1) and (1, -2) has slope
Determine if line A is perpendicular to line B.
, are not negative reciprocals so the lines are
Be careful! The lines do look
perpendicular. But the relationship
between their slopes tells us the lines are