Question 388685


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,0\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=0}}}.

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



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



{{{d=sqrt((2-3)^2+(0--3)^2)}}} Plug in {{{x[1]=2}}},  {{{x[2]=3}}}, {{{y[1]=0}}}, and {{{y[2]=-3}}}.



{{{d=sqrt((-1)^2+(0--3)^2)}}} Subtract {{{3}}} from {{{2}}} to get {{{-1}}}.



{{{d=sqrt((-1)^2+(3)^2)}}} Subtract {{{-3}}} from {{{0}}} to get {{{3}}}.



{{{d=sqrt(1+(3)^2)}}} Square {{{-1}}} to get {{{1}}}.



{{{d=sqrt(1+9)}}} Square {{{3}}} to get {{{9}}}.



{{{d=sqrt(10)}}} Add {{{1}}} to {{{9}}} to get {{{10}}}.



{{{d=1*sqrt(10)}}} Simplify the square root.



So our answer is {{{d=sqrt(10)}}} 



Which approximates to {{{d=3.162}}} 



So the distance between the two points is approximately 3.162 units. 



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