Question 316268
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-4,9\right)]. So this means that {{{x[1]=-4}}} and {{{y[1]=9}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,-3\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=-3}}}.



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



{{{d=sqrt((-4-1)^2+(9--3)^2)}}} Plug in {{{x[1]=-4}}},  {{{x[2]=1}}}, {{{y[1]=9}}}, and {{{y[2]=-3}}}.



{{{d=sqrt((-5)^2+(9--3)^2)}}} Subtract {{{1}}} from {{{-4}}} to get {{{-5}}}.



{{{d=sqrt((-5)^2+(12)^2)}}} Subtract {{{-3}}} from {{{9}}} to get {{{12}}}.



{{{d=sqrt(25+(12)^2)}}} Square {{{-5}}} to get {{{25}}}.



{{{d=sqrt(25+144)}}} Square {{{12}}} to get {{{144}}}.



{{{d=sqrt(169)}}} Add {{{25}}} to {{{144}}} to get {{{169}}}.



{{{d=13}}} Take the square root of {{{169}}} to get {{{13}}}.



So our answer is {{{d=13}}} 



So the distance between the two points is  13 units.