#include <bits/stdc++.h>

using namespace std;
#define ll long long
#define pii pair<int, int>
#define ld long double
#define all(a) (a).begin(), (a).end()

struct Vector {
    ld x;
    ld y;

    Vector(ld x = 0, ld y = 0): x(x), y(y) {}
    Vector(const Vector& a, const Vector& b): x(b.x - a.x), y(b.y - a.y) {}

    ld sqlen() { return x * x + y * y; }
};

Vector operator-(const Vector& a, const Vector& b) {
    return Vector(b, a);
}

Vector operator+(const Vector& a, const Vector& b) {
    return Vector(a.x + b.x, a.y + b.y);
}

Vector operator*(const Vector& a, ld k) {
    return Vector(a.x * k, a.y * k);
}

ld operator*(const Vector& a, const Vector& b) {
    return a.x * b.x + a.y * b.y;
}

istream& operator>>(istream& in, Vector& v) {
    in >> v.x >> v.y;
    return in;
}

void solve() {
    Vector o, a, b, c;
    cin >> o >> a >> c >> b;
    a = a - o;
    b = b - o;
    Vector o1, a1, b1, c1;
    cin >> o1 >> a1 >> c1 >> b1;
    a1 = a1 - o1;
    b1 = b1 - o1;
    Vector s, t;
    cin >> s >> t;

    auto tp = [&](Vector v) {
        v = v - o;
        return o1 + a1 * ((a * v) / (a * a)) + b1 * ((b * v) / (b * b));
    };

    int k, n;
    cin >> k >> n;
    vector<Vector> tps(n + 1), tpt(n + 1);
    tps[0] = s; tpt[0] = t;
    for (int i = 1; i <= n; ++i) {
        tps[i] = tp(tps[i - 1]);
        tpt[i] = tp(tpt[i - 1]);
    }
    ld ans = 1e18;
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= n - i; ++j) {
            ans = min(ans, k * (i + j) + sqrtl((tps[i] - tpt[j]).sqlen()));
        }
    }
    cout << ans << "\n";
}

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    cout << fixed << setprecision(20);

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

    return 0;
}