#include<bits/stdc++.h>
using namespace std;
 
const int N=1e5+5;
const double pi=acos(-1.0);
const double eps=1e-12;
int sign(double x){
	if(fabs(x)<eps)return 0;
	return (x<0)?-1:1;
}
int dcmp(double x,double y){return sign(x-y);}

struct Point{
	double x,y;
	Point(double X=0,double Y=0):x(X),y(Y){}
	inline void in(){scanf("%lf%lf",&x,&y);}
	inline void out(){printf("%.2lf %.2lf\n",x,y);}
	Point operator + (const Point &r) const{return Point(x+r.x,y+r.y);}
	Point operator - (const Point &r) const{return Point(x-r.x,y-r.y);}
	Point operator * (double p) const{return Point(x*p,y*p);}
	Point operator / (double p) const{return Point(x/p,y/p);}
	bool operator < (const Point &r) const{return x<r.x||(x==r.x&&y<r.y);}
	bool operator == (const Point &r) const{return sign(x-r.x)==0&&sign(y-r.y)==0;}
};
typedef Point Vector;
double dot(Vector A,Vector B){return A.x*B.x+A.y*B.y;} 
double cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}
double length(Vector A){return sqrt(dot(A,A));}
double dis(Point A,Point B){return length(A-B);}
double angle(Vector A,Vector B){return acos(dot(A,B)/length(A)/length(B));}
double project(Point a,Point b,Point c){return dot(b-a,c-a)/length(b-a);}
double polar_angle(Vector A){return atan2(A.y,A.x);}
double area(Point a,Point b,Point c){return cross(b-a,c-a);}
Vector rotate(Vector A,double rad){
	return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}

struct Line{
	Point a,b;
	Vector v;
	double r;
	Line(){} 
	Line(const Point &A,const Point &B,int op=0){
		if(!op){a=A,b=B;v=b-a;r=polar_angle(v);}
		else {a=A,v=B;b=a+v;r=polar_angle(v);}
	}
	Point point(double p){return a+v*p;}
	bool line_inc(const Point &p) const{return sign(cross(p-a,v))==0;}
	bool seg_inc(const Point &p) const{
		return sign(cross(a-p,b-p))==0&&sign(dot(a-p,b-p))<=0;
	}
};
typedef Line Seg;
Point point_line_proj(Point p,Line l){
	return l.a+l.v*(dot(l.v,p-l.a)/dot(l.v,l.v));
}
double point_to_line(Point p,Line l){
	return fabs(cross(l.v,p-l.a))/length(l.v);
}
double point_to_seg(Point p,Seg s){
	if(s.a==s.b)return length(p-s.a);
	Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b;
	if(sign(dot(v1,v2))<0)return length(v2);
	if(sign(dot(v1,v3))>0)return length(v3);
	return point_to_line(p,Line(s.a,s.b)); 
}
Point line_line_inter(Line x,Line y){//记得先判平行 
	Vector U=x.a-y.a;
	double t=cross(y.v,U)/cross(x.v,y.v);//注意方向 
	return x.a+x.v*t;
}
bool seg_seg_inter(Seg x,Seg y){
	Point a1=x.a,a2=x.b,b1=y.a,b2=y.b;
    double c1=cross(a2-a1,b1-a1),c2=cross(a2-a1,b2-a1),
           c3=cross(b2-b1,a1-b1),c4=cross(b2-b1,a2-b1);
    return sign(c1)*sign(c2)<=0&&sign(c3)*sign(c4)<=0;
}
bool line_seg_inter(Line x,Seg y){
	Point a1=x.a,a2=x.b,b1=y.a,b2=y.b;
    double c1=cross(a2-a1,b1-a1),c2=cross(a2-a1,b2-a1);
    return sign(c1)*sign(c2)<=0;
}

struct Circle{
	Point o;double r;
	Circle(){}
	Circle(const Point &O,double R):o(O),r(R){}
	bool inc(const Point &p){
		return dcmp(r,dis(o,p))>=0;
	}
};
Line get_line(Point a,Point b){return Line((a+b)/2,rotate(b-a,pi/2),1);};
Circle get_circle(Point a,Point b,Point c){
	Line u=get_line(a,b),v=get_line(a,c);
	Point o=line_line_inter(u,v);
	return Circle(o,dis(o,a));
}
Circle min_circle(Point p[],int n){
	random_shuffle(p,p+n);
	Circle c=Circle(p[0],0);
	for(int i=1;i<n;i++)
		if(!c.inc(p[i])){
			c=Circle(p[i],0);
			for(int j=0;j<i;j++)
				if(!c.inc(p[j])){
					c=Circle((p[i]+p[j])/2,dis(p[i],p[j])/2);
					for(int k=0;k<j;k++)
						if(!c.inc(p[k]))
							c=get_circle(p[i],p[j],p[k]);
				}
		}
	return c;
}

double poly_area(Point p[],int n){
    double res=0;
    for(int i=1;i<n-1;i++) 
        res+=cross(p[i]-p[0],p[i+1]-p[0]);
    return res/2;
}

int top,st[N];
void Andrew(Point p[],int cnt){
	vector<bool>used(cnt);
	sort(p+1,p+1+cnt);
	for(int i=1;i<=cnt;i++){
		while(top>1&&area(p[st[top-1]],p[st[top]],p[i])<=0)used[st[top--]]=0;
		st[++top]=i;used[i]=1;
	}
	used[1]=0;
	for(int i=cnt;i;i--){
		if(used[i])continue;
		while(top>1&&area(p[st[top-1]],p[st[top]],p[i])<=0)top--;
		st[++top]=i;
	}
}

double rotating_caliper(Point p[]){
	double res=0;
	for(int i=1,a=3;i<top;i++){
		Point d=p[st[i]],e=p[st[i+1]];
		while(dcmp(area(d,e,p[st[a]]),area(d,e,p[st[a+1]]))<0)a=a%(top-1)+1;
		res=max(res,max(dis(d,p[st[a]]),dis(e,p[st[a]])));
	}
	return res;
}

bool cmp(const Line& x,const Line& y){
	if(sign(x.r-y.r)==0)return area(x.a,x.b,y.b)<0; 
	return x.r<y.r;
}
bool on_right(Line a,Line b,Line c){
	Point o=line_line_inter(b,c);
	return sign(area(a.a,a.b,o))<=0;
}
double half_plane_inter(Line l[],int cnt){
	sort(l+1,l+1+cnt,cmp);
	int L=0,R=-1;
	vector<int>q(cnt);
	for(int i=1;i<=cnt;i++){
		if(i>1&&sign(l[i].r-l[i-1].r)==0)continue;
		while(L+1<=R&&on_right(l[i],l[q[R-1]],l[q[R]]))R--;
		while(L+1<=R&&on_right(l[i],l[q[L]],l[q[L+1]]))L++;
		q[++R]=i;
	}
	while(L+1<=R&&on_right(l[q[L]],l[q[R-1]],l[q[R]]))R--;
	while(L+1<=R&&on_right(l[q[R]],l[q[L]],l[q[L+1]]))L++;
	q[++R]=q[L];
	vector<Point>ans(R);
	int k=0;
	for(int i=L;i<R;i++)
		ans[++k]=line_line_inter(l[q[i]],l[q[i+1]]);
	double res=0;
	for(int i=2;i+1<=k;i++)res+=area(ans[1],ans[i],ans[i+1]);
	return res/2;
}
double solve()
{
    Point a,b,c,d;
    Point A,B,C,D;
    a.in(),b.in(),c.in(),d.in();
    A.in(),B.in(),C.in(),D.in();
    Point beg,ed;
    beg.in(),ed.in();
    double k;int n;
    scanf("%lf%d",&k,&n);
    vector<Point> s(n+1),t(n+1);
    s[0]=beg,t[0]=ed;
    for(int i=1;i<=n;i++){
        s[i]=A+(B-A)*(dot(s[i-1]-a,b-a)/dot(b-a,b-a))+(D-A)*(dot(s[i-1]-a,d-a)/dot(d-a,d-a));
        t[i]=A+(B-A)*(dot(t[i-1]-a,b-a)/dot(b-a,b-a))+(D-A)*(dot(t[i-1]-a,d-a)/dot(d-a,d-a));
    }
    double ans=2e9;
    for(int i=0;i<=n;i++){
        for(int j=0;j+i<=n;j++){
            ans=min(ans,k*((double)(i+j))+dis(s[i],t[j]));
        }
    }
    return ans;
}
int main()
{
    int T;scanf("%d",&T);while(T--)printf("%.12lf\n",solve());
}