Question 422495
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-2,4\right)]. So this means that {{{x[1]=-2}}} and {{{y[1]=4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,10\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=10}}}.



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



{{{d=sqrt((-2-6)^2+(4-10)^2)}}} Plug in {{{x[1]=-2}}},  {{{x[2]=6}}}, {{{y[1]=4}}}, and {{{y[2]=10}}}.



{{{d=sqrt((-8)^2+(4-10)^2)}}} Subtract {{{6}}} from {{{-2}}} to get {{{-8}}}.



{{{d=sqrt((-8)^2+(-6)^2)}}} Subtract {{{10}}} from {{{4}}} to get {{{-6}}}.



{{{d=sqrt(64+(-6)^2)}}} Square {{{-8}}} to get {{{64}}}.



{{{d=sqrt(64+36)}}} Square {{{-6}}} to get {{{36}}}.



{{{d=sqrt(100)}}} Add {{{64}}} to {{{36}}} to get {{{100}}}.



{{{d=10}}} Take the square root of {{{100}}} to get {{{10}}}.



So our answer is {{{d=10}}} 



So the distance between the two points is  10 units. 



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