What is the slope of any line perpendicular to the line passing through #(14,2)# and #(9,5)#?

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Answer 1 · 2015-12-30T12:54:59

The slope of the perpendicular is #5/3# The explanation is given below.

Slope #m# of any line passing through two given points #(x_1,y_1)# and #(x_2,y_2)# is given by

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

The slope of perpendicular would be negative reciprocal of this slope.

#m_p = -(x_2-x_1)/(y_2-y1)#

Our given points are #(14,2)# and #(9,5)#

#x_1=14#, #y_1=2#
#x_2=9#, #y_2=5#

The slope of any line perpendicular to the line joining #(14,2)# and #(9.5)# is given by.

#m_p = -(9-14)/(5-2)#
#m_p = -(-5)/3#
#m_p=5/3#

The slope of the perpendicular is #5/3#