Given data:
The coordinate of Lily;s house is (-2, 2).
The coordinate of Mike's house is (-4, 2).
The coordinate of library is (4,6)
The cordinate of mid point is,
((-2-4)/2, (2+2)/2))=(-3,2)
The distance between mid point to the Library is,
The distance they need to travel is (65)^(1/2) miles.