Question 330311


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(-4,5\right)].  So this means that {{{x[2]=-4}}} and {{{y[2]=5}}}.



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



{{{d=sqrt((3--4)^2+(-2-5)^2)}}} Plug in {{{x[1]=3}}},  {{{x[2]=-4}}}, {{{y[1]=-2}}}, and {{{y[2]=5}}}.



{{{d=sqrt((7)^2+(-2-5)^2)}}} Subtract {{{-4}}} from {{{3}}} to get {{{7}}}.



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



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



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



{{{d=sqrt(98)}}} Add {{{49}}} to {{{49}}} to get {{{98}}}.



{{{d=7*sqrt(2)}}} Simplify the square root.



So our answer is {{{d=7*sqrt(2)}}} 



Since {{{d=b*sqrt(2)}}} and {{{d=7*sqrt(2)}}}, this means that {{{b*sqrt(2)=7*sqrt(2)}}}



So {{{b=7}}}