#include<bits/stdc++.h>
#define Ri register int
#define D long double 
using namespace std;
const int N=123;
const D inf=1e8,eps=1e-9;
struct pt{
	D x,y;
};
pt operator + (const pt x,const pt y){
	pt z;
	z.x=x.x+y.x;
	z.y=x.y+y.y;
	return z;
}
pt operator - (const pt x,const pt y){
	pt z;
	z.x=x.x-y.x;
	z.y=x.y-y.y;
	return z;
}
pt operator * (const D x,const pt y){
	pt z;
	z.x=y.x*x;
	z.y=y.y*x;
	return z;
}
struct nd{
	D A,B,C,sq;
	void gg(){
		sq=sqrt(A*A+B*B);
	}
};
D dis(const pt x,const pt y){
	return sqrt((x.x-y.x)*(x.x-y.x)+(x.y-y.y)*(x.y-y.y));
}
D Dis(const pt x,const nd y){
	return fabs(x.x*y.A+x.y*y.B+y.C)/y.sq;
}
nd get(const pt x,const pt y){//
	nd O;
	if(fabs(x.y-y.y)<eps){
		O.A=0,O.B=-1,O.C=y.y;
		return O;
	}
	if(fabs(x.x-y.x)<eps){
		O.A=-1,O.B=0,O.C=x.x;
		return O;
	}
	double k=(x.y-y.y)/(x.x-y.x),b=x.y-x.x*k;
//	if(fabs(b-(y.y-y.x*k))>eps) printf("!!!!");
	O.A=k,O.B=-1,O.C=b;
	return O;
}
struct jz{
	pt a[5];
	nd b[5];
	D di[5];
	void pr(){
		for(Ri i=1; i<=4; ++i){
			di[i]=dis(a[i],a[i%4+1]);
		}
		for(Ri i=1; i<=4; ++i){
			b[i]=get(a[i],a[i%4+1]);
			b[i].gg();
//			if(fabs(a[i%4+1].x*b[i].A+a[i%4+1].y*b[i].B+b[i].C)>eps) printf("?");
//			printf("%Lf %Lf %Lf\n",b[i].A,b[i].B,b[i].C);
		}
	}
}A[3];
pt aa[N],bb[N];
D ans;
int n,K;
pt trs(pt X){//
	double aa=Dis(X,A[1].b[1])/A[1].di[2],bb=Dis(X,A[1].b[4])/A[1].di[1];
	pt Y=A[2].a[1]+aa*(A[2].a[4]-A[2].a[1])+bb*(A[2].a[2]-A[2].a[1]);
//	double cc=Dis(Y,A[2].b[1])/A[2].di[2],dd=Dis(Y,A[2].b[4])/A[2].di[1];
//	if(fabs(aa-cc)>eps || fabs(bb-dd)>eps){
//		printf("???");
//	}
	return Y;
}
void ext(pt x[N]){
	for(Ri i=1; i<=n; ++i) x[i]=trs(x[i-1]);
}
void Sol(){
	for(Ri i=1; i<=2; ++i){
		for(Ri j=1; j<=4; ++j) scanf("%Lf %Lf",&A[i].a[j].x,&A[i].a[j].y);
		A[i].pr();
	}
	scanf("%Lf %Lf %Lf %Lf",&aa[0].x,&aa[0].y,&bb[0].x,&bb[0].y);
	scanf("%d %d",&K,&n);
	ans=inf;
	ext(aa),ext(bb);
	for(Ri i=0; i<=n; ++i){
		for(Ri j=0; j+i<=n; ++j){
			ans=min(ans,dis(aa[i],bb[j])+(i+j)*K);
		}
	}
	printf("%Lf\n",ans);
}
int main(){
	int T;
	scanf("%d",&T);
	while(T--) Sol();
}