Question 243523
Remember that the perpendicular slope is the negative reciprocal of the original slope. So flip {{{5/12}}} to get {{{12/5}}} and change the sign to get {{{-12/5}}}. So the perpendicular slope is {{{m=-12/5}}}



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



{{{-12/5=(-8-4)/(x--4)}}} Plug in {{{m=-12/5}}}, {{{y[2]=-8}}}, {{{y[1]=4}}}, {{{x[2]=x}}}, and {{{x[1]=-4}}}



{{{-12/5=(-8-4)/(x+4)}}} Rewrite {{{x--4}}} as {{{x+4}}}



{{{-12/5=(-12)/(x+4)}}} Combine like terms.



{{{-12(x+4)=5(-12)}}} Cross multiply.



{{{-12x-12(4)=5(-12)}}} Distribute



{{{-12x-48=-60}}} Multiply



{{{-12x=-60+48}}} Add {{{48}}} to both sides.



{{{-12x=-12}}} Combine like terms on the right side.



{{{x=(-12)/(-12)}}} Divide both sides by {{{-12}}} to isolate {{{x}}}.



{{{x=1}}} Reduce.



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Answer:


So the solution is {{{x=1}}}