解：
1) 对于点D，B(4,2)，C(3,5)，BD:DC = 1:2，所以λ = 1/2
[
begin{aligned}
x_D &= frac{x_B + lambda x_C}{1 + lambda} = frac{4 + frac{1}{2} imes 3}{1 + frac{1}{2}} = frac{4 + 1.5}{1.5} = frac{5.5}{1.5} = frac{11}{3}
y_D &= frac{y_B + lambda y_C}{1 + lambda} = frac{2 + frac{1}{2} imes 5}{1 + frac{1}{2}} = frac{2 + 2.5}{1.5} = frac{4.5}{1.5} = 3
end{aligned}
]
所以D点坐标为 (left(frac{11}{3}, 3
ight))
2) A(1,1)，D(11/3, 3)，求AD的长度：
[
begin{aligned}
AD &= sqrt{left(frac{11}{3} - 1
ight)^2 + (3 - 1)^2}
&= sqrt{left(frac{8}{3}
ight)^2 + 2^2}
&= sqrt{frac{64}{9} + 4}
&= sqrt{frac{64}{9} + frac{36}{9}}
&= sqrt{frac{100}{9}} = frac{10}{3}
end{aligned}
]
所以中线AD的长度为 (frac{10}{3})
