What is the slope of any line perpendicular to the line passing through #(13,17)# and #(-1,-2)#?

1 Answer
Mar 5, 2018

Answer:

See a solution process below:

Explanation:

First, we can 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)(-2) - color(blue)(17))/(color(red)(-1) - color(blue)(13)) = (-19)/-14 = 19/14#

One of the characteristics of perpendicular lines is their slopes are the negative inverse of each other. In other words, if the slope of one line is: #m#

Then the slope of the perpendicular line, let's call it #m_p#, is

#m_p = -1/m#

We can calculate the slope of a perpendicular line as:

#m_p = -1/(19/14) = -14/19#

Any line perpendicular to the line in the problem will have a slope of:

#m = -14/19#