#include<bits/stdc++.h>
#define rep(i,s,n) for (int i = (int)(s); i < (int)(n); i++)
#define all(v) begin(v),end(v)
using namespace std;
using ll = long long;
bool chmin(auto &a, auto b){ return a > b ? a = b, 1 : 0; }
bool chmax(auto &a, auto b){ return a < b ? a = b, 1 : 0; }

double dist(double x1, double y1, double x2, double y2) {
    return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

typedef pair<double,double> pd;

void solve() {
    vector<double> x1(4), y1(4);
    vector<double> x2(4), y2(4);
    rep(i,0,4) cin >> x1[i] >> y1[i];
    rep(i,0,4) cin >> x2[i] >> y2[i];
    double sx, sy, tx, ty;
    cin >> sx >> sy;
    cin >> tx >> ty;
    double getax = x1[0];
    double getay = y1[0];
    sx -= getax;
    sy -= getay;
    tx -= getax;
    ty -= getay;
    rep(i,0,4) {
        x1[i] -= getax;
        y1[i] -= getay;
        x2[i] -= getax;
        y2[i] -= getay;
    }


    double k; cin >> k;
    int n; cin >> n;

    pd va1, va2, vb1, vb2;
    va1 = pair(x1[1] - x1[0], y1[1] - y1[0]);
    va2 = pair(x1[3] - x1[0], y1[3] - y1[0]);
    vb1 = pair(x2[1] - x2[0], y2[1] - y2[0]);
    vb2 = pair(x2[3] - x2[0], y2[3] - y2[0]);

    vector ma(2, vector<double>(2));
    ma[0][0] = va2.second;
    ma[0][1] = -va2.first;
    ma[1][0] = -va1.second;
    ma[1][1] = va1.first;

    double det = va1.first * va2.second - va1.second * va2.first;
    rep(i,0,2) rep(j,0,2) {
        ma[i][j] /= det;
    }

    vector<pd> sgo(n + 1), tgo(n + 1);
    sgo[0] = pair(sx, sy);
    tgo[0] = pair(tx, ty);
    auto f = [&](pd x) -> pd {
        vector<double> factor(2);
        factor[0] += ma[0][0] * x.first;
        factor[0] += ma[0][1] * x.second;
        factor[1] += ma[1][0] * x.first;
        factor[1] += ma[1][1] * x.second;
        pd ans;
        ans.first = factor[0] * vb1.first + factor[1] * vb2.first + x2[0];
        ans.second = factor[0] * vb1.second + factor[1] * vb2.second + y2[0];
        return ans;
    };

    for (int i=1; i<=n; i++) { 
        sgo[i] = f(sgo[i-1]);
        tgo[i] = f(tgo[i-1]);
        //cout << sgo[i].first << ' ' << sgo[i].second << endl;
    }

    double ret = 9e18;
    rep(i,0,n+1) {
        rep(j,0,n+1-i) {
            double tmp = k * (i + j);
            tmp += dist(sgo[i].first, sgo[i].second, tgo[j].first, tgo[j].second);
            chmin(ret, tmp);
        }
    }

    cout << ret << '\n';



}

int main(){
    cin.tie(0)->sync_with_stdio(0);

    cout << fixed << setprecision(15);   
    int t;
    cin >> t;
    while(t--) {
        solve();
    }
}