#include<bits/stdc++.h>
using namespace std;using ll=long long;const int M=998244353;const double eps=1e-10,inf=1e30;
struct Im_num
{
	double re,im;void ini(double y,double x){re=y,im=x;}
	Im_num(double y=0,double x=0){ini(y,x);}
	void outp(){cout<<re<<"|"<<im<<'\n'; }
};
Im_num add(Im_num a,Im_num b){return Im_num(a.re+b.re,a.im+b.im);}
Im_num sub(Im_num a,Im_num b){return Im_num(a.re-b.re,a.im-b.im);}
Im_num mul(Im_num a,Im_num b){return Im_num(a.re*b.re-a.im*b.im,a.re*b.im+a.im*b.re);}
double mol(Im_num a){return a.re*a.re+a.im*a.im; }
Im_num inv(Im_num a){double L=mol(a);return Im_num(a.re/L,-a.im/L);}
Im_num div(Im_num a,Im_num b){return mul(a,inv(b)); }
struct S
{
	Im_num B[2][4];bool fl;Im_num a,b,xA,xB,xC;double y,x,k,res;int n;
	vector<Im_num>S,E;
	void solve()
	{
		for(int e=0;e<2;e++)for(int i=0;i<4;i++)cin>>x>>y,B[e][i].ini(x,y);a=sub(B[0][1],B[0][0]);b=sub(B[1][1],B[1][0]);
		xA=sub(B[0][3],B[0][0]),xB=mul(xA,b),xA=sub(B[1][3],B[1][0]),xC=mul(xA,a);xA=sub(xB,xC);fl=(abs(xA.re)>eps||abs(xA.im)>eps);
		S.resize(1);cin>>x>>y,S[0].ini(x,y);E.resize(1);cin>>x>>y,E[0].ini(x,y);cin>>k>>n;
		S.resize(n+1);for(int i=1;i<=n;i++){xA=sub(S[i-1],B[0][0]);xA=div(xA,a);if(fl)xA.im*=-1;xA=mul(xA,b);S[i]=add(xA,B[1][0]);}
		E.resize(n+1);for(int i=1;i<=n;i++){xA=sub(E[i-1],B[0][0]);xA=div(xA,a);if(fl)xA.im*=-1;xA=mul(xA,b);E[i]=add(xA,B[1][0]);}
		res=inf;for(int i=0;i<=n;i++)for(int j=0;j<=n-i;j++)res=min(res,k*(i+j)+sqrt(mol(sub(S[i],E[j]))));cout<<res<<'\n';
	}
};
void precal()
{
	
}
int main()
{
	//freopen("1.in","r",stdin);
	cout<<fixed<<setprecision(12);
	ios::sync_with_stdio(0);cin.tie(0);precal();
	int t=1;cin>>t;
	//clock_t a=clock();
	while(t--){S SS;SS.solve();}
	//cout<<"Time:"<<double(clock()-a)<<'\n';
}