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

using ll = long long;
using pii = pair<int, int>;

const double eps = 1e-8;

template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	bool operator==(P p) const { return fabs(x-p.x)<=eps&&fabs(y-p.y)<=eps; }
	bool operator!=(P p) const { return fabs(x-p.x)>eps||fabs(y-p.y)>eps; }
	T dist2() const { return x*x + y*y; }
	double dist() const { return sqrt((double)dist2()); }

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

void solve() {
	Point<double> a1, b1, c1, d1;
	Point<double> a2, b2, c2, d2;
	cin >> a1.x >> a1.y >> b1.x >> b1.y >> c1.x >> c1.y >> d1.x >> d1.y;
	cin >> a2.x >> a2.y >> b2.x >> b2.y >> c2.x >> c2.y >> d2.x >> d2.y;

	Point<double> db1, dd1, db2, dd2;
	db1 = b1 - a1, dd1 = d1 - a1;
	assert(a1 + db1 + dd1 == c1);
	db2 = b2 - a2, dd2 = d2 - a2;
	assert(a2 + db2 + dd2 == c2);

	auto f = [&](const Point<double> &pt) {
		Point<double> diff = pt - a1;
		double k1 = (diff.x * dd1.y - diff.y * dd1.x) / (db1.x * dd1.y - db1.y * dd1.x);
		double k2 = (diff.x - k1 * db1.x) / dd1.x;
		assert(0 <= k1 + eps && k1 - eps <= 1);
		assert(0 <= k2 + eps && k2 - eps <= 1);
		return a2 + db2 * k1 + dd2 * k2;
	};

	Point<double> S, T;
	cin >> S.x >> S.y >> T.x >> T.y;
	double k;
	int n;
	cin >> k >> n;
	vector<Point<double>> ST(n + 1), TT(n + 1);
	ST[0] = S, TT[0] = T;
	for (int i = 1; i <= n; i++) {
		ST[i] = f(ST[i - 1]);
		TT[i] = f(TT[i - 1]);
		// cout << ST[i] << " " << TT[i] << "\n";
	}

	double ans = 1e18;
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j <= n; j++) {
			if (i + j > n) break;
			double cur = k * (i + j);
			cur += (ST[i] - TT[j]).dist();
			ans = min(ans, cur);
		}
	}
	cout << fixed << setprecision(9) << ans << "\n";
}

int main() {
	cin.tie(0)->sync_with_stdio(0);
	int t;
	cin >> t;
	while (t--) {
		solve();
	}
}