Question 316270
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,-3\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=-3}}}.

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



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



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



{{{d=sqrt(9+(-4)^2)}}} Square {{{3}}} to get {{{9}}}.



{{{d=sqrt(9+16)}}} Square {{{-4}}} to get {{{16}}}.



{{{d=sqrt(25)}}} Add {{{9}}} to {{{16}}} to get {{{25}}}.



{{{d=5}}} Take the square root of {{{25}}} to get {{{5}}}.



So our answer is {{{d=5}}} 



So the distance between the two points is  5 units.