Question 97277
First find the length of the line segment from W to M



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(5,3\right)] and *[Tex \Large \left(x_{2}, y_{2}\right)] is the second point *[Tex \Large \left(-10,-5\right)]


{{{d=sqrt((5--10)^2+(3--5)^2)}}} Plug in {{{x[1]=5}}}, {{{x[2]=-10}}}, {{{y[1]=3}}}, {{{y[2]=-5}}}


{{{d=sqrt((15)^2+(8)^2)}}} Evaluate {{{5--10}}} to get 15. Evaluate {{{3--5}}} to get 8. 


{{{d=sqrt(225+64)}}} Square each value


{{{d=sqrt(289)}}} Add


{{{d=17}}} 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 (5,3) and (-10,-5) is 17 units




Since the length of the segment through W and M is 17 units, simply double the length to get the total length of the segment



17*2=34



So the total length is 34 units