Question 293490

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

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



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



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



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



{{{d=sqrt((4)^2+(-3)^2)}}} Subtract {{{-2}}} from {{{-5}}} 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 is  5 units.