#include <bits/stdc++.h>  
using namespace std;  

#define int long long  

using db = double;
constexpr db eps = 1e-9;

int sgn(db x) {
    if (x > eps) {
        return 1;
    } else if (x < -eps) {
        return -1;
    }
    return 0;
}

struct Point {
    db x, y;
    Point operator+(const Point &p) const {
        return {x + p.x, y + p.y};
    }
    Point operator-(const Point &p) const {
        return {x - p.x, y - p.y};
    }
    Point operator*(const db &k) const {
        return {x * k, y * k};
    }
    Point operator/(const db &k) const {
        return {x / k, y / k};
    }

    db len2() {
        return x * x + y * y;
    }
    db len() {
        return sqrt(len2());
    }

    friend ostream &operator<<(ostream &os, Point &p) {
        os << "(" << p.x << ", " << p.y << ")";
        return os;
    }
};

db cross(Point a, Point b) {
    return a.x * b.y - a.y * b.x;
}

db dot(Point a, Point b) {
    return a.x * b.x + a.y * b.y;
}

Point proj(Point p, Point a, Point b) {
    Point k = b - a;
    return a + k * (dot(p - a, k) / k.len2());
}

db dis(Point a, Point b) {
    return (b - a).len();
}

void solve() {
    vector<Point> a(4), b(4);

    for (auto &[x, y] : a) {
        cin >> x >> y;
    }
    for (auto &[x, y] : b) {
        cin >> x >> y;
    }
    
    Point s, t;
    cin >> s.x >> s.y >> t.x >> t.y;

    db k;
    int n;
    cin >> k >> n;

    auto trans1 = [&](Point p) {
        Point px = proj(p, a[0], a[1]), py = proj(p, a[0], a[3]);
        db lx = (px - a[0]).len() / (a[1] - a[0]).len(), ly = (py - a[0]).len() / (a[3] - a[0]).len();
        return b[0] + (b[1] - b[0]) * lx + (b[3] - b[0]) * ly;
    };
    
    auto trans2 = [&](Point p) {
        Point px = proj(p, b[0], b[1]), py = proj(p, b[0], b[3]);
        db lx = (px - b[0]).len() / (b[1] - b[0]).len(), ly = (py - b[0]).len() / (b[3] - b[0]).len();
        return a[0] + (a[1] - a[0]) * lx + (a[3] - a[0]) * ly;
    };

    auto inMap = [&](Point p) {
        vector<int> pd(4);
        for (int i = 0; i < 4; i++) {
            pd[i] = sgn(cross(b[(i + 1) % 4] - b[i], p - b[i]));
        }
        for (int i = 0; i < 4; i++) {
            for (int j = i + 1; j < 4; j++) {
                if (pd[i] * pd[j] < 0) {
                    return false;
                }
            }
        }
        return true;
    };

    vector<Point> s1{s}, t1{t};
    for (int i = 1; i <= n; i++) {
        s1.push_back(trans1(s1.back()));
        t1.push_back(trans1(t1.back()));
    }
    // for (int i = 0; i <= n; i++) {
    //     cout << s1[i] << " \n"[i == n];
    // }
    // for (int i = 0; i <= n; i++) {
    //     cout << t1[i] << " \n"[i == n];
    // }
    vector<Point> s2{s}, t2{t};
    for (int i = 1; i <= n; i++) {
        if (!inMap(s2.back())) {
            break;
        }
        s2.push_back(trans2(s2.back()));
    }
    for (int i = 1; i <= n; i++) {
        if (!inMap(t2.back())) {
            break;
        }
        t2.push_back(trans2(t2.back()));
    }
    // for (int i = 0; i < s2.size(); i++) {
    //     cout << s2[i] << " \n"[i + 1 == s2.size()];
    // }
    // for (int i = 0; i < t2.size(); i++) {
    //     cout << t2[i] << " \n"[i + 1 == t2.size()];
    // }

    db ans = 1e100;
    for (int i = 0; i < s1.size(); i++) {
        for (int j = 0; j < t1.size(); j++) {
            if (i + j <= n) {
                ans = min(ans, (i + j) * k + dis(s1[i], t1[j]));
            }    
        }
    }
    for (int i = 0; i < s2.size(); i++) {
        for (int j = 0; j < t1.size(); j++) {
            if (i + j <= n) {
                ans = min(ans, (i + j) * k + dis(s2[i], t1[j]));
            }    
        }
    }
    for (int i = 0; i < s1.size(); i++) {
        for (int j = 0; j < t2.size(); j++) {
            if (i + j <= n) {
                ans = min(ans, (i + j) * k + dis(s1[i], t2[j]));
            }    
        }
    }
    for (int i = 0; i < s2.size(); i++) {
        for (int j = 0; j < t2.size(); j++) {
            if (i + j <= n) {
                ans = min(ans, (i + j) * k + dis(s2[i], t2[j]));
            }    
        }
    }
    
    cout << ans << "\n";
}

signed main() {  
    ios::sync_with_stdio(false);
    cin.tie(nullptr);  

    cout << fixed << setprecision(10);

    int t;
    cin >> t;
    while (t--) {
        solve();
    }    

    return 0;
}