求平行四邊形的第四個點的坐標

Given are the (x,y) coordinates of the endpoints of two adjacent sides of a parallelogram. Find the (x,y) coordinates of the fourth point.

Input

Each line of input contains eight floating point numbers: the (x,y) coordinates of one of the endpoints of the first side followed by the (x,y) coordinates of the other endpoint of the first side, followed by the (x,y) coordinates of one of the endpoints of the second side followed by the (x,y) coordinates of the other endpoint of the second side. All coordinates are in meters, to the nearest mm. All coordinates are between -10000 and +10000.

Output

For each line of input, print the (x,y) coordinates of the fourth point of the parallelogram in meters, to the nearest mm, separated by a single space.

Sample Input

0.000 0.000 0.000 1.000 0.000 1.000 1.000 1.000
1.000 0.000 3.500 3.500 3.500 3.500 0.000 1.000
1.866 0.000 3.127 3.543 3.127 3.543 1.412 3.145

Sample Output

1.000 0.000
-2.500 -2.500
0.151 -0.398

題意 ：給你平行四邊形的相鄰的兩條邊，讓你求第四個點的坐標
思路分析：一個比較基礎的計算幾何題，只要根據向量的矢量和相等即可求解
　　　　相等的點的位置有 4 種情況，分別是 1 3、 1 4、 2 3、 2 4分別求即可
代碼示例 ：

struct point
{
    double x, y;
    point(double _x=0, double _y=0):x(_x), y(_y){}
     
    // 點-點=向量
    point operator-(const point &v){
        return point(x-v.x, y-v.y);
    }
 
};
 
int dcmp(double x){
    if (fabs(x)<eps) return 0;
    else return x<0?-1:1;
}
bool operator == (const point &a, const point &b){
    return (dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0);
}
 
typedef point Vector; // Vector表示向量

point p[10];

int main() {
    //freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
    
    while(~scanf("%lf%lf", &p[1].x, &p[1].y)){
        for(int i = 2; i <= 4; i++) {
            scanf("%lf%lf", &p[i].x, &p[i].y);
        }
        
        if (p[2] == p[3]) {
            Vector v = p[4] - p[3];
            printf("%.3f %.3f\n", v.x+p[1].x, v.y+p[1].y);
        }
        if (p[2] == p[4]){
            Vector v = p[3] - p[4];
            printf("%.3f %.3f\n", v.x+p[1].x, v.y+p[1].y);
        }
        if (p[1] == p[3]){
            Vector v = p[4]-p[3];
            printf("%.3f %.3f\n", v.x+p[2].x, v.y+p[2].y);
        }
        if (p[1] == p[4]){
            Vector v = p[3] - p[4];
            printf("%.3f %.3f\n", v.x+p[2].x, v.y+p[2].y);
        }
    }
    return 0;
}