Question 550447


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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,1\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=1}}}.



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



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



{{{d=sqrt((-7)^2+(2-1)^2)}}} Subtract {{{4}}} from {{{-3}}} to get {{{-7}}}.



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



{{{d=sqrt(49+(1)^2)}}} Square {{{-7}}} to get {{{49}}}.



{{{d=sqrt(49+1)}}} Square {{{1}}} to get {{{1}}}.



{{{d=sqrt(50)}}} Add {{{49}}} to {{{1}}} to get {{{50}}}.



{{{d=5*sqrt(2)}}} Simplify the square root.



So our answer is {{{d=5*sqrt(2)}}} 



Which approximates to {{{d=7.071}}} 



So the distance between the two points is approximately 7.071 units. 



So the exact length of RT is {{{5*sqrt(2)}}} units which is approximately 7.071 units.