Question 207328
I'll do the first one to get you started.



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-5,-7\right)].  So this means that {{{x[2]=-5}}} and {{{y[2]=-7}}}.



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



{{{d=sqrt((-1--5)^2+(-4--7)^2)}}} Plug in {{{x[1]=-1}}},  {{{x[2]=-5}}}, {{{y[1]=-4}}}, and {{{y[2]=-7}}}.



{{{d=sqrt((4)^2+(-4--7)^2)}}} Subtract {{{-5}}} from {{{-1}}} to get {{{4}}}.



{{{d=sqrt((4)^2+(3)^2)}}} Subtract {{{-7}}} from {{{-4}}} to get {{{3}}}.



{{{d=sqrt(16+(3)^2)}}} Square {{{4}}} to get {{{16}}}.



{{{d=sqrt(16+9)}}} Square {{{3}}} to get {{{9}}}.



{{{d=sqrt(25)}}} Add {{{16}}} to {{{9}}} 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 *[Tex \LARGE \left(-1,-4\right)] and *[Tex \LARGE \left(-5,-7\right)] is 5 units.