Question 321301
Step 1) Find the slope of the line through the points (10, 18) and (6, 10)



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(10,18\right)]. So this means that {{{x[1]=10}}} and {{{y[1]=18}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,10\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=10}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(10-18)/(6-10)}}} Plug in {{{y[2]=10}}}, {{{y[1]=18}}}, {{{x[2]=6}}}, and {{{x[1]=10}}}



{{{m=(-8)/(6-10)}}} Subtract {{{18}}} from {{{10}}} to get {{{-8}}}



{{{m=(-8)/(-4)}}} Subtract {{{10}}} from {{{6}}} to get {{{-4}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(10,18\right)] and *[Tex \LARGE \left(6,10\right)] is {{{m=2}}}


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Step 2) Take the reciprocal of the given slope and change the sign. 



Since the slope of the line that goes through the points *[Tex \LARGE \left(10,18\right)] and *[Tex \LARGE \left(6,10\right)] is {{{m=2}}}, which can be written as {{{m=2/1}}}, we can flip the fraction and then change the sign to get the perpendicular slope of {{{m=-1/2}}}



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Answer:



The slope of ANY line perpendicular to the line that goes through the points *[Tex \LARGE \left(10,18\right)] and *[Tex \LARGE \left(6,10\right)] is {{{-1/2}}} making the answer a)