Question 104656
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(-9,3\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(-1,-5\right)]


{{{d=sqrt((-9--1)^2+(3--5)^2)}}} Plug in {{{x[1]=-9}}}, {{{x[2]=-1}}}, {{{y[1]=3}}}, {{{y[2]=-5}}}


{{{d=sqrt((-8)^2+(8)^2)}}} Evaluate {{{-9--1}}} to get -8. Evaluate {{{3--5}}} to get 8. 


{{{d=sqrt(64+64)}}} Square each value


{{{d=sqrt(128)}}} Add


{{{d=8*sqrt(2)}}} 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=11.3137084989848}}}


which rounds to

11.31


So the distance between (-9,3) and (-1,-5) is approximately 11.31 units