Question 90343
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(-3,-2\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(1,4\right)]


{{{d=sqrt((-3-1)^2+(-2-4)^2)}}} Plug in {{{x[1]=-3}}}, {{{x[2]=1}}}, {{{y[1]=-2}}}, {{{y[2]=4}}}


{{{d=sqrt((-4)^2+(-6)^2)}}} Evaluate {{{-3-1}}} to get -4. Evaluate {{{-2-4}}} to get -6. 


{{{d=sqrt(16+36)}}} Square each value


{{{d=sqrt(52)}}} Add


{{{d=2*sqrt(13)}}} Simplify the square root



Which approximates to


{{{d=7.21110255092798}}}


which rounds to

7.21


So the distance between (-3,-2) and (1,4) is approximately 7.21 units