#include<iostream>
#include<cstring>
#include<vector>
#include<cmath>
#include<iomanip>
using namespace std;
using LL = long long;
using point_t = long double; //全局数据类型，可修改为 long long 等

const point_t eps = 1e-8;
const long double PI = acosl(-1);
//const long double PI = numbers::pi_v<long double>;

// 点与向量
template <typename T>
struct point{
    T x, y;

    void input(){
        int xx, yy;
        cin >> xx >> yy;
        x = xx, y = yy;
    }

    bool operator==(const point &a) const { return (abs(x - a.x) <= eps && abs(y - a.y) <= eps); }
    bool operator<(const point &a) const{
        if (abs(x - a.x) <= eps)
            return y < a.y - eps;
        return x < a.x - eps;
    }
    bool operator>(const point &a) const { return !(*this < a || *this == a); }
    point operator+(const point &a) const { return {x + a.x, y + a.y}; }
    point operator-(const point &a) const { return {x - a.x, y - a.y}; }
    point operator-() const { return {-x, -y}; }
    point operator*(const T k) const { return {k * x, k * y}; }
    point operator/(const T k) const { return {x / k, y / k}; }
    T operator*(const point &a) const { return x * a.x + y * a.y; } // 点积
    T operator^(const point &a) const { return x * a.y - y * a.x; } // 叉积，注意优先级
    int toleft(const point &a) const
    {
        const auto t = (*this) ^ a;
        return (t > eps) - (t < -eps);
    }                                                             // to-left 测试
    T len2() const { return (*this) * (*this); }                  // 向量长度的平方
    T dis2(const point &a) const { return (a - (*this)).len2(); } // 两点距离的平方

    // 涉及浮点数
    long double len() const { return sqrtl(len2()); }                                                                      // 向量长度
    long double dis(const point &a) const { return sqrtl(dis2(a)); }                                                       // 两点距离
    long double ang(const point &a) const { return acosl(max(-1.0l, min(1.0l, ((*this) * a) / (len() * a.len())))); }      // 向量夹角
    point rot(const long double rad) const { return {x * cosl(rad) - y * sinl(rad), x * sinl(rad) + y * cosl(rad)}; }          // 逆时针旋转（给定角度）
    point rot(const long double cosr, const long double sinr) const { return {x * cosr - y * sinr, x * sinr + y * cosr}; } // 逆时针旋转（给定角度的正弦与余弦）
};

using Point = point<point_t>;

struct Plane{
    Point o, vx, vy;
    double len1, len2;  
}r[2];

int main(){

#ifdef LOCAL
    freopen("data.in", "r", stdin);
    freopen("data.out", "w", stdout);
#endif

    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);

    int T;
    cin >> T;
    while(T--){
        for(int i = 0; i < 2; i++){
            Point p[4];
            for(int j = 0; j < 4; j++){
                p[j].input();
            }
            long double len1 = (p[3] - p[0]).len();
            long double len2 = (p[1] - p[0]).len();
            r[i] = {p[0], (p[3] - p[0]) / len1, (p[1] - p[0]) / len2, len1, len2};
        }

        auto get = [&](Point p){
            auto v = p - r[0].o;
            double t1 = v * r[0].vx / r[0].len1 * r[1].len1;
            double t2 = v * r[0].vy / r[0].len2 * r[1].len2;
            Point ret = r[1].o + r[1].vx * t1 + r[1].vy * t2;
            return ret;
        };

        Point s, t;
        s.input(), t.input();
        int k, n;
        cin >> k >> n;

        vector<Point> path1{s}, path2{t};
        for(int i = 0; i <= n; i++){
            path1.push_back(get(path1.back()));
            path2.push_back(get(path2.back()));
        }
        long double ans = 1e18;
        for(int i = 0; i <= n; i++){
            for(int j = 0; i + j <= n; j++){
                ans = min(ans, 1.0L * k * (i + j) + path1[i].dis(path2[j]));
            }
        }
        cout << ans << '\n';
    }

}