Question 121916
Do you want to find the distance between these points?


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


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


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


{{{d=sqrt(9+81)}}} 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 (2,-5) and (5,4) is approximately 9.49 units