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

##### 1 Answer

Mar 7, 2016

#### 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 perpendicularthen 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 #