Question 89146
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(11,-6\right)] and *[Tex \Large \left(x_{2},y_{2}\right)] is the second point *[Tex \Large \left(-1,-2\right)]


{{{d=sqrt((11--1)^2+(-6--2)^2)}}} Plug in {{{x[1]=11}}}, {{{x[2]=-1}}}, {{{y[1]=-6}}}, {{{y[2]=-2}}}


{{{d=sqrt((12)^2+(-4)^2)}}} Evaluate {{{11--1}}} to get 12. Evaluate {{{-6--2}}} to get -4. 


{{{d=sqrt(144+16)}}} Square each value


{{{d=sqrt(160)}}} Add


{{{d=4*sqrt(10)}}} Simplify the square root



Which approximates to


{{{d=12.6491106406735}}}


which rounds to

12.65


So the distance between (11,-6) and (-1,-2) is about 12.65