Question 452761


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,-2\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=-2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,4\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=4}}}.



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



{{{d=sqrt((5--3)^2+(-2-4)^2)}}} Plug in {{{x[1]=5}}},  {{{x[2]=-3}}}, {{{y[1]=-2}}}, and {{{y[2]=4}}}.



{{{d=sqrt((8)^2+(-2-4)^2)}}} Subtract {{{-3}}} from {{{5}}} to get {{{8}}}.



{{{d=sqrt((8)^2+(-6)^2)}}} Subtract {{{4}}} from {{{-2}}} to get {{{-6}}}.



{{{d=sqrt(64+(-6)^2)}}} Square {{{8}}} to get {{{64}}}.



{{{d=sqrt(64+36)}}} Square {{{-6}}} to get {{{36}}}.



{{{d=sqrt(100)}}} Add {{{64}}} to {{{36}}} to get {{{100}}}.



{{{d=10}}} Take the square root of {{{100}}} to get {{{10}}}.



So our answer is {{{d=10}}} 



So the distance between the two points is  10 units.