#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
#define TIME (clock() * 1.0 / CLOCKS_PER_SEC)

struct vect {
    ld x, y;

    vect() = default;
    vect(ld x, ld y) : x(x), y(y) {}

    vect operator-(const vect& other) const {
        return vect(x - other.x, y - other.y);
    }

    ld operator*(const vect& other) const {
        return x * other.x + y * other.y;
    }

    ld len() const {
        return hypotl(x, y);
    }

    vect operator*(ld cf) const {
        return vect(x * cf, y * cf);
    }

    vect operator+(const vect& other) const {
        return vect(x + other.x, y + other.y);
    }
};

istream& operator>>(istream& in, vect& a) {
    int x, y;
    in >> x >> y;
    a.x = x;
    a.y = y;
    return in;
}

ostream& operator<<(ostream& out, const vect& a) {
    return out << a.x << " " << a.y;
}

void solve() {
    vector<vect> v1(4), v2(4);
    for (int i = 0; i < 4; i++) {
        cin >> v1[i];
    }
    for (int i = 0; i < 4; i++) {
        cin >> v2[i];
    }

    ld lenx = (v1[0] - v1[1]).len();
    ld leny = (v1[2] - v1[1]).len();

    auto transform = [&](const vect& pt) {
        ld cx = ((pt - v1[1]) * (v1[0] - v1[1])) / (lenx * lenx);
        ld cy = ((pt - v1[1]) * (v1[2] - v1[1])) / (leny * leny);
        return v2[1] + (v2[0] - v2[1]) * cx + (v2[2] - v2[1]) * cy;
    };

    vect s, t;
    cin >> s >> t;

    int k, n;
    cin >> k >> n;

    vector<vect> seq1(n + 1);
    seq1[0] = s;
    for (int i = 1; i <= n; i++) {
        seq1[i] = transform(seq1[i - 1]);
    }
    vector<vect> seq2(n + 1);
    seq2[0] = t;
    for (int i = 1; i <= n; i++) {
        seq2[i] = transform(seq2[i - 1]);
    }

    ld ans = 1e18;
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= n - i; j++) {
            ans = min(ans, (seq1[i] - seq2[j]).len() + (ld)k * (i + j));
        }
    }

    cout << ans << "\n";
}

int main() {
#ifdef ONPC
    freopen("input", "r", stdin);
#endif
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

    cout << fixed << setprecision(20);

    int t = 1;
    cin >> t;
    while (t--) {
        solve();
    }

    return 0;
}