Question 458611


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(23,-33\right)]. So this means that {{{x[1]=23}}} and {{{y[1]=-33}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,9\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=9}}}.



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



{{{d=sqrt((23-4)^2+(-33-9)^2)}}} Plug in {{{x[1]=23}}},  {{{x[2]=4}}}, {{{y[1]=-33}}}, and {{{y[2]=9}}}.



{{{d=sqrt((19)^2+(-33-9)^2)}}} Subtract {{{4}}} from {{{23}}} to get {{{19}}}.



{{{d=sqrt((19)^2+(-42)^2)}}} Subtract {{{9}}} from {{{-33}}} to get {{{-42}}}.



{{{d=sqrt(361+(-42)^2)}}} Square {{{19}}} to get {{{361}}}.



{{{d=sqrt(361+1764)}}} Square {{{-42}}} to get {{{1764}}}.



{{{d=sqrt(2125)}}} Add {{{361}}} to {{{1764}}} to get {{{2125}}}.



{{{d=5*sqrt(85)}}} Simplify the square root.



So our answer is {{{d=5*sqrt(85)}}} 



Which approximates to {{{d=46.098}}} (after using a calculator)



So the distance between the two points is approximately 46.098 units.