Question 114436
Start with the given distance formula

{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} where *[Tex \Large \left(x_{1}, y_{1}\right)] is the first point *[Tex \Large \left(5,1\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(3,8\right)]


{{{d=sqrt((5-3)^2+(1-8)^2)}}} Plug in {{{x[1]=5}}}, {{{x[2]=3}}}, {{{y[1]=1}}}, {{{y[2]=8}}}


{{{d=sqrt((2)^2+(-7)^2)}}} Evaluate {{{5-3}}} to get 2. Evaluate {{{1-8}}} to get -7. 


{{{d=sqrt(4+49)}}} Square each value


{{{d=sqrt(53)}}} Add


So the distance approximates to


{{{d=7.28010988928052}}}


which rounds to

7.28


So the distance between (5,1) and (3,8) is approximately 7.28 units