Question 139482
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(5,8\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(-4,5\right)]


{{{d=sqrt((5--4)^2+(8-5)^2)}}} Plug in {{{x[1]=5}}}, {{{x[2]=-4}}}, {{{y[1]=8}}}, {{{y[2]=5}}}


{{{d=sqrt((9)^2+(3)^2)}}} Evaluate {{{5--4}}} to get 9. Evaluate {{{8-5}}} to get 3. 


{{{d=sqrt(81+9)}}} Square each value


{{{d=sqrt(90)}}} Add


{{{d=3*sqrt(10)}}} Simplify the square root  (note: If you need help with simplifying the square root, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)



So the distance approximates to


{{{d=9.48683298050514}}}


which rounds to

9.49


So the distance between (5,8) and (-4,5) is approximately 9.49 units