Question 256137
We basically want to find the distance from R(-2,1) to  S(-1,3)



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,1\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=1}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,3\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=3}}}.



{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((-2--1)^2+(1-3)^2)}}} Plug in {{{x[1]=-2}}},  {{{x[2]=-1}}}, {{{y[1]=1}}}, and {{{y[2]=3}}}.



{{{d=sqrt((-1)^2+(1-3)^2)}}} Subtract {{{-1}}} from {{{-2}}} to get {{{-1}}}.



{{{d=sqrt((-1)^2+(-2)^2)}}} Subtract {{{3}}} from {{{1}}} to get {{{-2}}}.



{{{d=sqrt(1+(-2)^2)}}} Square {{{-1}}} to get {{{1}}}.



{{{d=sqrt(1+4)}}} Square {{{-2}}} to get {{{4}}}.



{{{d=sqrt(5)}}} Add {{{1}}} to {{{4}}} to get {{{5}}}.



So our answer is {{{d=sqrt(5)}}} which means that the length of RS is {{{sqrt(5)}}} units.