Question 323224


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-3,5\right)]. So this means that {{{x[1]=-3}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,-8\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=-8}}}.



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



{{{d=sqrt((-3-5)^2+(5--8)^2)}}} Plug in {{{x[1]=-3}}},  {{{x[2]=5}}}, {{{y[1]=5}}}, and {{{y[2]=-8}}}.



{{{d=sqrt((-8)^2+(5--8)^2)}}} Subtract {{{5}}} from {{{-3}}} to get {{{-8}}}.



{{{d=sqrt((-8)^2+(13)^2)}}} Subtract {{{-8}}} from {{{5}}} to get {{{13}}}.



{{{d=sqrt(64+(13)^2)}}} Square {{{-8}}} to get {{{64}}}.



{{{d=sqrt(64+169)}}} Square {{{13}}} to get {{{169}}}.



{{{d=sqrt(233)}}} Add {{{64}}} to {{{169}}} to get {{{233}}}.



So our answer is {{{d=sqrt(233)}}} 



Which approximates to {{{d=15.264}}} (using a calculator)




So the distance between the two points A and B is exactly {{{sqrt(233)}}} units.



and the approximate distance between the two points A and B is about 15.264 units.