acm 2 1006 Line belt
1.1006
2.
Problem Description
In a two-dimensional plane there are two line belts, there are two segments AB and CD, lxhgww's speed on AB is P and on CD is Q, he can move with the speed R on other area on the plane.
How long must he take to travel from A to D?
How long must he take to travel from A to D?
Input
The first line is the case number T.
For each case, there are three lines.
The first line, four integers, the coordinates of A and B: Ax Ay Bx By.
The second line , four integers, the coordinates of C and D:Cx Cy Dx Dy.
The third line, three integers, P Q R.
0<= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy<=1000
1<=P，Q，R<=10
For each case, there are three lines.
The first line, four integers, the coordinates of A and B: Ax Ay Bx By.
The second line , four integers, the coordinates of C and D:Cx Cy Dx Dy.
The third line, three integers, P Q R.
0<= Ax，Ay，Bx，By，Cx，Cy，Dx，Dy<=1000
1<=P，Q，R<=10
Output
The minimum time to travel from A to D, round to two decimals.
Sample Input
1
0 0 0 100
100 0 100 100
2 2 1
0 0 0 100
100 0 100 100
2 2 1
Sample Output
136.60
3.在二维平面上有两线带，有两段AB和CD，lxhgww的速度对AB是P，在CD是Q，他用速度R在其他地区在平面上移动。多久他从A到D？
4.先三分AB上的点，再三分CD上的点
证明：
设E在AB上，F在CD上。
AB 时间：f = AE / p，
Z和Y 时间：g = EF / r + FD / q。
f单调递增，而g先递减后递增。
两个函数叠加，所得的函数先递减后递增,所以用三分法
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