What is the slope of any line perpendicular to the line passing through #(9,15)# and #(7,2)#?

2 Answers
crayon
Apr 10, 2018

#-2/13#

Explanation:

Let the slope of the line joining the 2 points be #m# and the slope of the line perpendicular to it be #m_1#.

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

#m=(15-2)/(9-7)=13/2#

We know, # mm_1=-1#

So #m_1=-2/13 # [ANS]

Jim G.
Apr 10, 2018

#"perpendicular slope "=-2/13#

Explanation:

#"calculate the slope m using the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(9,15)" and "(x_2,y_2)=(7,2)#

#rArrm=(2-15)/(7-9)=(-13)/(-2)=13/2#

#"Given a line with slope m then the slope of a line"#
#"perpendicular to it is"#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#rArr"perpendicular slope "=-1/(13/2)=-2/13#

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