What is the equation of the line that is perpendicular to the line passing through #(-5,-6)# and #(4,-10)# at midpoint of the two points?

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Answer 1 · 2016-03-31T02:49:15

Equation of the line #18x-8y=55#

From the given two points #(-5, -6)# and #(4, -10)#, we need to obtain first the negative reciprocal of the slope m and the midpoint of the points.

Let start with the midpoint #(x_m, y_m)#

#x_m=(x_1+x_2)/2=(-5+4)/2=-1/2#
#y_m=(y_1+y_2)/2=(-6+(-10))/2=-8#

midpoint #(x_m, y_m)=(-1/2, -8)#

Negative reciprocal of the slope # m_p=-1/m#

# m_p=-1/m=(-1)/((-10--6)/(4--5))=(-1)/(-4/9)=9/4#

The equation of the line

#y-y_m=m_p(x-x_m)#

#y--8=9/4(x--1/2)#
#y+8=9/4(x+1/2)#
#4y+32=9x+9/2#

#8y+64=18x+9#

#18x-8y=55#

God bless....I hope the explanation is useful.