What is the slope of any line perpendicular to the line passing through #(-12,14)# and #(-1,1)#?

1 Answer
May 1, 2017

Answer:

See the solution process below:

Explanation:

First, find the slope of the line defined by 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)(1) - color(blue)(14))/(color(red)(-1) - color(blue)(-12)) = (color(red)(1) - color(blue)(14))/(color(red)(-1) + color(blue)(12)) = -13/11#

Let's call the slope of the perpendicular line #m_p#

The formula for #m_p# is:

#m_p = -1/m#

Substituting the slope we calculated for #m# and calculating #m_p# gives:

#m_p = (-1)/(-13/11) = 11/13#

The slope of a perpendicular line is #11/13#