Question 388681


Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,5\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,-7\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=-7}}}.



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



{{{d=sqrt((0--3)^2+(5--7)^2)}}} Plug in {{{x[1]=0}}},  {{{x[2]=-3}}}, {{{y[1]=5}}}, and {{{y[2]=-7}}}.



{{{d=sqrt((3)^2+(5--7)^2)}}} Subtract {{{-3}}} from {{{0}}} to get {{{3}}}.



{{{d=sqrt((3)^2+(12)^2)}}} Subtract {{{-7}}} from {{{5}}} to get {{{12}}}.



{{{d=sqrt(9+(12)^2)}}} Square {{{3}}} to get {{{9}}}.



{{{d=sqrt(9+144)}}} Square {{{12}}} to get {{{144}}}.



{{{d=sqrt(153)}}} Add {{{9}}} to {{{144}}} to get {{{153}}}.



{{{d=3*sqrt(17)}}} Simplify the square root.



So the exact distance is {{{d=3*sqrt(17)}}} 



Which approximates to {{{d=12.369}}} 



So the distance between the two points is approximately 12.369 units. 



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