#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
using namespace std;

#define LOG(f...) fprintf(stderr, f)

using db = long double;

struct pt {
  db x, y;
};
pt operator+(pt a, pt b) { return {a.x + b.x, a.y + b.y}; }
pt operator-(pt a, pt b) { return {a.x - b.x, a.y - b.y}; }
pt operator*(db l, pt a) { return {l * a.x, l * a.y}; }
db dot(pt a, pt b) { return a.x * b.x + a.y * b.y; }
db len(pt a) { return hypot(a.x, a.y); }

pt A[4], B[4];

pt F(pt P) {
  pt i = A[1] - A[0], j = A[3] - A[0];
  i = ((db)1 / len(i) / len(i)) * i;
  j = ((db)1 / len(j) / len(j)) * j;
  db ci = dot((P - A[0]), i);
  db cj = dot((P - A[0]), j);
  return B[0] + ci * (B[1] - B[0]) + cj * (B[3] - B[0]);
}

int main() {
  // freopen("input.txt", "r", stdin);
  // freopen("output.txt", "w", stdout);
  int T;
  scanf("%d", &T);
  while (T--) {
    for (auto &x : A)
      scanf("%Lf%Lf", &x.x, &x.y);
    for (auto &x : B)
      scanf("%Lf%Lf", &x.x, &x.y);
    pt S, T;
    scanf("%Lf%Lf%Lf%Lf", &S.x, &S.y, &T.x, &T.y);
    db k, n;
    scanf("%Lf%Lf", &k, &n);
    vector<pt> fS(n + 1), fT(n + 1);
    fS[0] = S; fT[0] = T;
    for (int i = 1; i <= n; ++i)
      fS[i] = F(fS[i - 1]);
    for (int i = 1; i <= n; ++i)
      fT[i] = F(fT[i - 1]);
    db ans = INFINITY;
    for (int i = 0; i <= n; ++i)
      for (int j = 0; j <= n - i; ++j)
        ans = min(ans, k * (i + j) + len(fS[i] - fT[j]));
    printf("%.18Lg\n", ans);
  }
}