Question 200921
A)


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point R *[Tex \LARGE \left(-2,3\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point S *[Tex \LARGE \left(5,1\right)].



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



{{{m=(1-3)/(5--2)}}} Plug in {{{y[2]=1}}}, {{{y[1]=3}}}, {{{x[2]=5}}}, and {{{x[1]=-2}}}



{{{m=(-2)/(5--2)}}} Subtract {{{3}}} from {{{1}}} to get {{{-2}}}



{{{m=(-2)/(7)}}} Subtract {{{-2}}} from {{{5}}} to get {{{7}}}



So the slope of the line that goes through the points R *[Tex \LARGE \left(-2,3\right)] and S *[Tex \LARGE \left(5,1\right)] is {{{m=-2/7}}}



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B)


Now simply flip the fraction {{{-2/7}}} to get {{{-7/2}}}. Finally, change the sign to get {{{7/2}}}. So the slope of ANY perpendicular line to segment RS is {{{m=7/2}}}