#include <bits/stdc++.h>
#define LOG(FMT...) fprintf(stderr, FMT);
#define rep(i, j, k) for(int i = j; i <= k; ++ i)
#define per(i, j, k) for(int i = j; i >= k; -- i)
using namespace std;

using db = long double;
using P = complex<db>;
const db eps = 1e-10;

P x;
P a[6], b[6];

db dist(P a, P b) {
  return abs(a - b);
}
void read(P &z) {
  db x, y;
  scanf("%Lf%Lf", &x, &y);
  z = P(x, y);
}
db det(P a, P b) {
  return a.real() * b.imag() - a.imag() * b.real();
}
bool eq(db a, db b) {
  return abs(a - b) < eps;
}
bool equal(P a, P b) {
  return eq(a.real(), b.real()) && eq(a.imag(), b.imag());
}
int main() {
  // freopen("1.in", "r", stdin);
  int test;
  scanf("%d", &test);
  rep(T, 1, test) {
    rep(i, 1, 4) read(b[i]); //b: park
    rep(i, 1, 4) read(a[i]); //a: map
    auto in = [&](P *a, P p) {
      bool z[2] = {0};
      rep(i, 1, 4) {
        P u = a[i], v = a[i == 4 ? 1 : i+1];
        db r = det(v - u, p - u);
        if(!eq(r, 0))
          z[r > 0] = true;
      }
      return !(z[0] && z[1]);
    };
    P x1 = a[1], x2 = a[2];
    P y1 = b[1], y2 = b[2];

    P p = (y1 - y2) / (x1 - x2);
    P p0 = (y1 - y2) / conj(x1 - x2);
    P q = y1 - p * x1, q0 = y1 - p0 * conj(x1);

    bool flag = true;

    auto F = [&](P z) {
      if(flag)
        return p * z + q;
      return p0 * conj(z) + q0;
    }; //map -> park
    auto G = [&](P z) {
      if(flag)
        return (z - q) / p;
      return conj((z - q0) / p0);
    }; //park -> map

    if(!equal(F(a[3]), b[3]) || !equal(F(a[4]), b[4])) {
      flag = false;
    }

    P s, t; read(s); read(t);

    int c, n;
    scanf("%d%d", &c, &n);
    db ans = dist(s, t);
    if(n) {
      vector<P> S(n + 1), T(n + 1);
      S[0] = s;
      T[0] = t;
      int p = 0;
      while(p + 1 <= n) {
        S[p+1] = G(S[p]);
        if(!in(b, S[p+1]))
          break;
        ++p;
      }
      int q = 0;
      while(q + 1 <= n) {
        T[q+1] = G(T[q]);
        if(!in(a, T[q+1]))
          break;
        ++q;
      }
      // printf("p = %d, q = %d\n", p, q);
      rep(i, 0, p)
        rep(j, 0, min(q, n - i))
          ans = min(ans, (i + j) * c + dist(S[i], T[j]));
    }
    printf("%.11Lf\n", ans);
  }
  return 0;
}