What is the slope of any line perpendicular to the line passing through #(24,-2)# and #(18,19)#?

1 Answer
Mar 7, 2016

Answer:

# m = 2/7#

Explanation:

The first step is to calculate the gradient (m) of the line joining the 2 points using the #color(blue)" gradient formula "#

# m = (y_2 - y_1)/(x_2 - x_1) #

where #(x_1,y_1) " and " (x_2,y_2) " are the coords of 2 points "#

let #(x_1,y_1) = (24,-2) " and " (x_2,y_2) = (18,19) #

substitute these values into formula for m.

#rArr m = (19+2)/(18-24) = 21/-6 = -7/2 #

Now if 2 lines with gradients # m_1 " and m_2# are perpendicular

then their product #m_1 . m_2 = -1 #

let # m_2 " be gradient of perpendicular line "#

#rArr m_2 = (-1)/m_1 = -1/(-7/2) = 2/7 #