What is the slope of any line perpendicular to the line passing through #(15,-22)# and #(12,-15)#?

1 Answer
Jim G.
Oct 2, 2016

#m=3/7#

Explanation:

Given 2 perpendicular lines with slopes #m_1" and " m_2# then

#color(red)(bar(ul(|color(white)(a/a)color(black)(m_1xxm_2=-1)color(white)(a/a)|)))#

We require to calculate #m_1# using the #color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#
where # (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"#

The 2 points here are (15 ,-22) and (12 ,-15)

#rArrm_1=(-15-(-22))/(12-15)=7/(-3)=-7/3#

Thus #-7/3xxm_2=-1#

#rArrm_2=(-1)/(-7/3)=3/7#

Hence the slope of any line perpendicular to the line passing through the 2 given points is #m=3/7#

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