What is the slope of any line perpendicular to the line passing through #(29,36)# and #(57,30)#?

1 Answer
smendyka
Jan 31, 2017

First, find the slope of the line passing through these two points. 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 of the points from the problem gives:

#m = (color(red)(30) - color(blue)(36))/(color(red)(57) - color(blue)(29))#

#m = (-6)/28 = -6/28 =-(2 xx 3)/(2 xx 14) = -3/14#

A line perpendicular to the line (let's call it #m_p#) will have the negative inverse slope or #m_p = -1/m#

Therefore #m_p = - -14/3 = 14/3#

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