Question 649314


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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,13\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=13}}}.



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



{{{d=sqrt((-3-7)^2+(1-13)^2)}}} Plug in {{{x[1]=-3}}},  {{{x[2]=7}}}, {{{y[1]=1}}}, and {{{y[2]=13}}}.



{{{d=sqrt((-10)^2+(1-13)^2)}}} Subtract {{{7}}} from {{{-3}}} to get {{{-10}}}.



{{{d=sqrt((-10)^2+(-12)^2)}}} Subtract {{{13}}} from {{{1}}} to get {{{-12}}}.



{{{d=sqrt(100+(-12)^2)}}} Square {{{-10}}} to get {{{100}}}.



{{{d=sqrt(100+144)}}} Square {{{-12}}} to get {{{144}}}.



{{{d=sqrt(244)}}} Add {{{100}}} to {{{144}}} to get {{{244}}}.



{{{d=2*sqrt(61)}}} Simplify the square root.



So the exact distance is {{{d=2*sqrt(61)}}} 



Which approximates to {{{d=15.62}}}