#include<bits/stdc++.h>
#define poly vector<int>
#define IOS ios::sync_with_stdio(false)
#define ll long long
#define double long double 
#define mp make_pair
#define mt make_tuple
#define pa pair < int,int >
#define fi first
#define se second
#define inf 1e18
#define mod 998244353
//#define int ll
//#define N
using namespace std;
struct point
{
	double x,y;
	double dis2() {return x*x+y*y;}
	double dis() {return sqrtl(dis2());}
	point(double X=0,double Y=0)
	{
		x=X,y=Y;
	}
	point friend operator + (point a,point b) {
		return (point){a.x+b.x,a.y+b.y};
	}
	point friend operator - (point a,point b) {
		return (point){a.x-b.x,a.y-b.y};
	}
	point friend operator * (point a,double b) {
		return (point){a.x*b,a.y*b};
	}
}A[15],a[15],s,t;
double mul(point a,point b) 
{
	return a.x*b.x+a.y*b.y;
}
double ans;
double k;
int n;
void BellaKira()
{
	for (int i=1;i<=4;i++)	
		cin>>a[i].x>>a[i].y;
	for (int i=1;i<=4;i++)	
		cin>>A[i].x>>A[i].y;
	cin>>s.x>>s.y>>t.x>>t.y>>k>>n;
	ans=inf;
	point lst=t;
	for (int i=0;i<=n;i++)
	{
		t=lst;
		for (int j=0;j<=n-i;j++)
		{
			ans=min(ans,(s-t).dis()+k*(i+j));
			t=A[1]+(A[2]-A[1])*(mul(t-a[1],a[2]-a[1])/(a[2]-a[1]).dis2())+
			(A[4]-A[1])*(mul(t-a[1],a[4]-a[1])/(a[4]-a[1]).dis2());
			// cout<<j<<" "<<t.x<<" "<<t.y<<'\n';
		}
		// cout<<'\n';
		s=A[1]+(A[2]-A[1])*(mul(s-a[1],a[2]-a[1])/(a[2]-a[1]).dis2())+
		(A[4]-A[1])*(mul(s-a[1],a[4]-a[1])/(a[4]-a[1]).dis2());
		// cout<<i<<" "<<s.x<<" "<<s.y<<'\n';
	}
	cout<<fixed<<setprecision(10)<<ans<<'\n';
}
signed main()
{
	IOS;
	cin.tie(0);
	int T=1;
	cin>>T;
	while (T--)
	{
		BellaKira();
	}
}