#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define ll long long
// #define int ll
#define pii pair<int,int>
#define se second
#define fi first
#define mpr make_pair
#define ull unsigned long long
// const int mod=1e9+7;
const int mod=998244353;
int add(int x,int y){
	x+=y;return x>=mod?x-mod:x;
}
void adto(int&x,int y){
	x+=y;
	x>=mod?x-=mod:x;
}
int mul(int x,int y){
	return 1ll*x*y%mod;
}
int qpow(int a,int b){
	int ans=1;
	while(b){
		if(b&1)ans=mul(ans,a);
		a=mul(a,a);
		b>>=1;
	}
	return ans;
}

#define db double
void done(db x,db y,db ix,db iy,db jx,db jy,db&x_,db&y_){
    x_=ix*x+jx*y;
    y_=iy*x+jy*y;
}
void redone(db x_,db y_,db ix,db iy,db jx,db jy,db&x,db&y){
    y=(ix*y_-iy*x_)/(ix*jy-iy*jx);
    x=(jy*x_-jx*y_)/(ix*jy-iy*jx);
}
db Ax,Ay,Bx,By,Cx,Cy,Dx,Dy;
db A_x,A_y,B_x,B_y,C_x,C_y,D_x,D_y;
db sx,sy,tx,ty;
db ix,iy,jx,jy;
db i_x,i_y,j_x,j_y;
int n,k;
const int maxn=444;
const db eps=1e-10;
db px[maxn],py[maxn],tp[maxn];
int s,t;
int pc;
int valid(db x,db y){
    return x>=-eps&&x<=1+eps&&y>=-eps&&y<=1+eps;
}
db dis(db ax,db ay,db bx,db by){
    return sqrt((ax-bx)*(ax-bx)+(ay-by)*(ay-by));
}
void solve(){
    cin>>Ax>>Ay>>Bx>>By>>Cx>>Cy>>Dx>>Dy;
    cin>>A_x>>A_y>>B_x>>B_y>>C_x>>C_y>>D_x>>D_y;
    cin>>sx>>sy>>tx>>ty;
    cin>>k>>n;
    pc=0;
    ++pc;px[pc]=sx,py[pc]=sy;s=pc;tp[pc]=0;
    ix=Dx-Ax,iy=Dy-Ay;
    jx=Bx-Ax,jy=By-Ay;
    i_x=D_x-A_x,i_y=D_y-A_y;
    j_x=B_x-A_x,j_y=B_y-A_y;
    for(int i=1;i<=n;i++){
        db tmpx,tmpy;
        sx-=Ax,sy-=Ay;
        redone(sx,sy,ix,iy,jx,jy,tmpx,tmpy);
            // cerr<<tmpx<<" "<<tmpy<<"  emm1\n";
        if(valid(tmpx,tmpy)){
            done(tmpx,tmpy,i_x,i_y,j_x,j_y,sx,sy);
            sx+=A_x;
            sy+=A_y;
            ++pc;px[pc]=sx,py[pc]=sy;tp[pc]=i;
        }
        else break;
    }
    sx=px[s],sy=py[s];
    for(int i=1;i<=n;i++){
        db tmpx,tmpy;
        sx-=A_x,sy-=A_y;
        redone(sx,sy,i_x,i_y,j_x,j_y,tmpx,tmpy);
        if(valid(tmpx,tmpy)){
            done(tmpx,tmpy,ix,iy,jx,jy,sx,sy);
            sx+=Ax;
            sy+=Ay;
            ++pc;px[pc]=sx,py[pc]=sy;tp[pc]=i;
        }
        else break;
    }
    ++pc;px[pc]=tx,py[pc]=ty;t=pc;tp[pc]=0;
    for(int i=1;i<=n;i++){
        db tmpx,tmpy;
        tx-=Ax,ty-=Ay;
        redone(tx,ty,ix,iy,jx,jy,tmpx,tmpy);
        if(valid(tmpx,tmpy)){
            done(tmpx,tmpy,i_x,i_y,j_x,j_y,tx,ty);
            tx+=A_x;
            ty+=A_y;
            ++pc;px[pc]=tx,py[pc]=ty;tp[pc]=i;
        }
        else break;
    }
    tx=px[t],ty=py[t];
    for(int i=1;i<=n;i++){
        db tmpx,tmpy;
        tx-=A_x,ty-=A_y;
        redone(tx,ty,i_x,i_y,j_x,j_y,tmpx,tmpy);
        if(valid(tmpx,tmpy)){
            done(tmpx,tmpy,ix,iy,jx,jy,tx,ty);
            tx+=Ax;
            ty+=Ay;
            ++pc;px[pc]=tx,py[pc]=ty;tp[pc]=i;
        }
        else break;
    }
    // cerr<<pc<<" \n";
    // for(int i=1;i<=pc;i++){
    //     cerr<<px[i]<<" "<<py[i]<<" "<<tp[i]<<"   emm\n";
    // }
    db ans=1e18;
    for(int i=s;i<t;i++){
        for(int j=t;j<=pc;j++){
            if(tp[i]+tp[j]<=n)
            ans=min(ans,dis(px[i],py[i],px[j],py[j])+k*(tp[i]+tp[j]));
        }
    }
    cout<<ans<<"\n";
}

signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0),cout.tie(0);
    cout<<fixed<<setprecision(20);
	int t=1;
	cin>>t;
	while(t--){
		solve();
	}
	// cerr<<1.*clock()/CLOCKS_PER_SEC<<"s...\n";
	return 0;
}