#include <bits/stdc++.h>
using namespace std;

template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;

using ll = int64_t;

#define pdd pair<double,double>
pdd a[5], b[5];
pdd d1,d2;
pdd s1,s2;
int k,n;
pdd s,t;

inline double dis(pdd p1, pdd p2)
{
	return sqrt((p1.first-p2.first)*(p1.first-p2.first)+(p1.second-p2.second)*(p1.second-p2.second));
}
inline double getval(pdd p1,pdd p2)
{
	return p1.first*p2.first+p1.second*p2.second;
}
inline double Len(pdd p)
{
	return (p.first*p.first+p.second*p.second);
}
inline pdd ask(pdd p)
{
	pdd d=pdd(p.first-a[1].first,p.second-a[1].second);
	return pdd(getval(d,d1)/Len(d1),getval(d,d2)/Len(d2));
}

pdd p1[105],p2[105];
int main() {
	ios_base::sync_with_stdio(false), cin.tie(nullptr);
	cout << fixed << setprecision(20);
	int T;
	cin>>T;
	while(T--)
	{
		for(int i=1;i<=4;i++) cin>>a[i].first>>a[i].second;
		for(int i=1;i<=4;i++) cin>>b[i].first>>b[i].second;

		d1=pdd(a[2].first-a[1].first,a[2].second-a[1].second);
		d2=pdd(a[4].first-a[1].first,a[4].second-a[1].second);

		s1=pdd(b[2].first-b[1].first,b[2].second-b[1].second);
		s2=pdd(b[4].first-b[1].first,b[4].second-b[1].second);

		cin>>s.first>>s.second>>t.first>>t.second;
		cin>>k>>n;
		p1[0]=s;
		for(int i=1;i<=n;i++)
		{
			pdd pos=ask(p1[i-1]);
			p1[i]=pdd(b[1].first+pos.first*s1.first+pos.second*s2.first,b[1].second+pos.first*s1.second+pos.second*s2.second);
		}
		p2[0]=t;
		for(int i=1;i<=n;i++) 
		{
			pdd pos=ask(p2[i-1]);
			//cout<<pos.first<<" "<<pos.second<<endl;
			p2[i]=pdd(b[1].first+pos.first*s1.first+pos.second*s2.first,b[1].second+pos.first*s1.second+pos.second*s2.second);
		}
		//cout<<p2[0].first<<" "<<p2[0].second<<endl;
		//cout<<p2[1].first<<" "<<p2[1].second<<endl;
		double ans=1e9;
		for(int i=0;i<=n;i++)
			for(int j=0;j+i<=n;j++)
			{
				ans=min(ans,dis(p1[i],p2[j])+(i+j)*k);
			}
		cout<<ans<<"\n";
	}
	return 0;
}