Question 356946


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(-5,1\right)].  So this means that {{{x[2]=-5}}} and {{{y[2]=1}}}.



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



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



{{{d=sqrt((8)^2+(-5-1)^2)}}} Subtract {{{-5}}} from {{{3}}} to get {{{8}}}.



{{{d=sqrt((8)^2+(-6)^2)}}} Subtract {{{1}}} from {{{-5}}} 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. 



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