What is the slope of any line perpendicular to the line passing through #(16,6)# and #(-2,-13)#?

Question

Julia Adams · Accepted Answer

#-18/19#

Let's first find the slope of the line passing through the aforementioned points

#(y_2-y_1)/(x_2-x_1) rarr# Finding a slope via two points formula

#(-13-6)/(-2-16) rarr# Plug in the points

#(-19)/-18#

#19/18 rarr# This is the slope of the line

Perpendicular slopes are opposite reciprocals of each other

To make something the opposite of another number, add a negative sign in front of it (a positive number's opposite will be negative, a negative number's opposite will be positive)

To find the reciprocal of a number, switch the numerator and denominator

#19/18#

#-19/18 rarr# The opposite

#-18/19 rarr# The (opposite) reciprocal

Nathan Axel · Answer

undefined The slope of any line perpendicular to a given line is the negative reciprocal of the slope of the given line. To find the slope of the given line passing through (16,6) and (-2,-13), we use the formula:

$$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

where $ (x_1, y_1) = (16,6) $ and $ (x_2, y_2) = (-2,-13) $.

$$ m = \frac{{-13 - 6}}{{-2 - 16}} = \frac{{-19}}{{-18}} = \frac{{19}}{{18}} $$

The slope of the given line is $ \frac{{19}}{{18}} $.

Therefore, the slope of any line perpendicular to the given line is the negative reciprocal of $ \frac{{19}}{{18}} $, which is $ -\frac{{18}}{{19}} $.