#include <bits/stdc++.h>

using namespace std;

long double m[3][4], a, b, c, d, e, f;

void s(long double &x, long double &y, long double &z)
{
    if (fabs(m[0][0]) < 1e-10) {
        if (fabs(m[1][0]) > 1e-10) {
            swap(m[0], m[1]);
        } else {
            swap(m[0], m[2]);
        }
    }
    double t = m[1][0] / m[0][0];
    m[1][0] -= m[0][0] * t;
    m[1][1] -= m[0][1] * t;
    m[1][2] -= m[0][2] * t;
    m[1][3] -= m[0][3] * t;
    t = m[2][0] / m[0][0];
    m[2][0] -= m[0][0] * t;
    m[2][1] -= m[0][1] * t;
    m[2][2] -= m[0][2] * t;
    m[2][3] -= m[0][3] * t;
    if (fabs(m[1][1]) < 1e-10) {
        swap(m[1], m[2]);
    }
    t = m[2][1] / m[1][1];
    m[2][1] -= m[1][1] * t;
    m[2][2] -= m[1][2] * t;
    m[2][3] -= m[1][3] * t;
    z = m[2][3] / m[2][2];
    y = (m[1][3] - m[1][2] * z) / m[1][1];
    x = (m[0][3] - m[0][2] * z - m[0][1] * y) / m[0][0];
    return;
}

void z(long double &x, long double &y)
{
    long double tx = x * a + y * b + c, ty = x * d + y * e + f;
    x = tx, y = ty;
    return;
}

signed main()
{
    int T;
    scanf("%d", &T);
    while (T--) {
        long double a, b, c, d, e, f, g, h, i, j, k, l;
        scanf("%Lf%Lf%Lf%Lf%Lf%Lf%*d%*d%Lf%Lf%Lf%Lf%Lf%Lf%*d%*d", &a, &b, &c, &d, &e, &f, &g, &h, &i, &j, &k, &l);
        m[0][0] = a, m[0][1] = b, m[0][2] = 1, m[0][3] = g;
        m[1][0] = c, m[1][1] = d, m[1][2] = 1, m[1][3] = i;
        m[2][0] = e, m[2][1] = f, m[2][2] = 1, m[2][3] = k;
        s(::a, ::b, ::c);
        m[0][0] = a, m[0][1] = b, m[0][2] = 1, m[0][3] = h;
        m[1][0] = c, m[1][1] = d, m[1][2] = 1, m[1][3] = j;
        m[2][0] = e, m[2][1] = f, m[2][2] = 1, m[2][3] = l;
        s(::d, ::e, ::f);
        scanf("%Lf%Lf%Lf%Lf", &a, &b, &c, &d);
        int n;
        scanf("%Lf%d", &k, &n);
        long double res = sqrt((a - c) * (a - c) + (b - d) * (b - d));
        for (int i = 0; i <= n; ++i) {
            e = c, f = d;
            for (int j = 0; j <= n - i; ++j) {
                res = min(res, (i + j) * k + sqrt((a - e) * (a - e) + (b - f) * (b - f)));
                z(e, f);
            }
            z(a, b);
        }
        printf("%.12Lf\n", res);
    }
    return 0;
}