Question 211521

Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,8\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=8}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,9\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=9}}}.




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



{{{d=sqrt((3--1)^2+(8-9)^2)}}} Plug in {{{x[1]=3}}},  {{{x[2]=-1}}}, {{{y[1]=8}}}, and {{{y[2]=9}}}.



{{{d=sqrt((4)^2+(8-9)^2)}}} Subtract {{{-1}}} from {{{3}}} to get {{{4}}}.



{{{d=sqrt((4)^2+(-1)^2)}}} Subtract {{{9}}} from {{{8}}} to get {{{-1}}}.



{{{d=sqrt(16+(-1)^2)}}} Square {{{4}}} to get {{{16}}}.



{{{d=sqrt(16+1)}}} Square {{{-1}}} to get {{{1}}}.



{{{d=sqrt(17)}}} Add {{{16}}} to {{{1}}} to get {{{17}}}.



So our answer is {{{d=sqrt(17)}}} 



Which approximates to {{{d=4.123}}} 



So the distance between the two points is approximately 4.123 units.