Question 109312
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,-7\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(0,5\right)]


{{{d=sqrt((5-0)^2+(-7-5)^2)}}} Plug in {{{x[1]=5}}}, {{{x[2]=0}}}, {{{y[1]=-7}}}, {{{y[2]=5}}}


{{{d=sqrt((5)^2+(-12)^2)}}} Evaluate {{{5-0}}} to get 5. Evaluate {{{-7-5}}} to get -12. 


{{{d=sqrt(25+144)}}} Square each value


{{{d=sqrt(169)}}} Add


{{{d=13}}} 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 between (5,-7) and (0,5) is 13 units