#include<bits/stdc++.h>
using namespace std;
#define IOS {cin.tie(0);cout.tie(0);ios::sync_with_stdio(0);}
#define rep(i,j,k) for(int i=j;i<=k;++i)
#define per(i,j,k) for(int i=j;i>=k;--i)
#define db long double
#define P pair<db,db>
const int N=105;
P operator + (P a,P b){return {a.first+b.first,a.second+b.second};}
P operator - (P a,P b){return {a.first-b.first,a.second-b.second};}
P operator * (P a,db k){return {a.first*k,a.second*k};}
db dis(P a,P b){return sqrt((a.first-b.first)*(a.first-b.first) + (a.second-b.second)*(a.second-b.second));}
P p[4],p1[4];
P qs[N],qt[N];
P sf(P pt){
    auto [a1,a2]=p[1]-p[0]; auto [b1,b2]=p[3]-p[0]; auto [c1,c2]=pt-p[0];
    db x=(c1*b2-c2*b1)/(a1*b2-a2*b1), y=(c1*a2-c2*a1)/(-a1*b2+a2*b1);
    // cout<<x<<' '<<y<<'\n';
    return (p1[1]-p1[0])*x+(p1[3]-p1[0])*y+p1[0];
}
void slv(){
    rep(i,0,3)cin>>p[i].first>>p[i].second;
    rep(i,0,3)cin>>p1[i].first>>p1[i].second;
    P s,t; cin>>s.first>>s.second >>t.first>>t.second;
    int k,n; cin>>k>>n;
    qs[0]=s; qt[0]=t;
    rep(i,1,n){
        qs[i]=sf(qs[i-1]); //cout<<qs[i].first<<' '<<qs[i].second<<'\n';
    }
    rep(i,1,n){
        qt[i]=sf(qt[i-1]); //cout<<qt[i].first<<' '<<qt[i].second<<'\n';
    }
    db ans=1e18;
    rep(i,0,n){
        rep(j,0,n-i){
            ans=min(ans,dis(qs[i],qt[j])+k*(i+j));
        }
    }
    cout<<ans<<'\n';
}
signed main(){
    IOS cout<<fixed<<setprecision(10);
    int T;cin>>T;
    while(T--)slv();
}
/*
1
0 0 0 3 6 3 6 0
0 1 1 0 3 2 2 3
0 0 4 2
0 3

0 0 0 2 4 2 4 0
0 0 0 1 2 1 2 0
2 1 4 2
1 1
*/