What is the slope of any line perpendicular to the line passing through #(2,-22)# and #(18,-4)#?

1 Answer
Feb 19, 2017

Answer:

Any line perpendicular to the line passing through these two points will have a slope of #-8/9#

Explanation:

First, we need to find the slope of the line passing through the two points in the problem. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.

Substituting the values from the points in the problem gives:

#m = (color(red)(-4) - color(blue)(-22))/(color(red)(18) - color(blue)(2)) = (color(red)(-4) + color(blue)(22))/(color(red)(18) - color(blue)(2)) = 18/16 = 9/8#

The slope of the line passing through the two points is #m = 9/8#

A line perpendicular to this line will have a slope (let's call it #m_p#) will have a slope which is the negative inverse of the slope of this line or:

#m_p = -1/m#

Or, #m_p = -8/9#