Problem:
Cross Point

For given two segments s1 and s2, print the coordinate of the cross point of them.

s1 is formed by end points p0 and p1, and
s2 is formed by end points p2 and p3.

Input

The entire input looks like:

q (the number of queries)
1st query
2nd query
...
qth query

Each query consists of integer coordinates of end points of s1 and s2 in the following format:

xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3

Output

For each query, print the coordinate of the cross point. The output values should be in a decimal fraction with an error less than 0.00000001.

Constraints

1 ≤ q ≤ 1000

-10000 ≤ xpi, ypi ≤ 10000

p0 ≠ p1 and
p2 ≠ p3.

The given segments have a cross point and are not in parallel.

Sample Input

3
0 0 2 0 1 1 1 -1
0 0 1 1 0 1 1 0
0 0 1 1 1 0 0 1

Sample Output

1.0000000000 0.0000000000
0.5000000000 0.5000000000
0.5000000000 0.5000000000

Solution in C# (judge verdict: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long q = long.Parse(Console.ReadLine());
    for(long i = 0; i < q; i++)
    {
      string[] input = Console.ReadLine().Split(' ');
      Vector2 vecA = new Vector2(decimal.Parse(input[0]), decimal.Parse(input[1]));
      Vector2 vecB = new Vector2(decimal.Parse(input[2]), decimal.Parse(input[3]));
      Vector2 vecAsub = new Vector2(decimal.Parse(input[4]), decimal.Parse(input[5]));
      Vector2 vecBsub = new Vector2(decimal.Parse(input[6]), decimal.Parse(input[7]));
      Vector2 answer = Vector2.IntersectPoint(vecA, vecB, vecAsub, vecBsub);
      Console.WriteLine(answer.x + " " + answer.y);//2線分の交点
    }
	}
}

class Vector2//2次元ベクトル
{
static decimal EPS = 1e-10m;//小数誤差比較

  public Vector2 (decimal X, decimal Y)
  {
    this.x = X;
    this.y = Y;
  }

  public decimal x {private set; get;}
  public decimal y {private set; get;}

  public static Vector2 operator + (Vector2 ob1, Vector2 ob2)//ベクトルの基本演算
  {
    return new Vector2 (ob1.x + ob2.x, ob1.y + ob2.y);
  }
  public static Vector2 operator - (Vector2 ob1, Vector2 ob2)
  {
    return new Vector2 (ob1.x - ob2.x, ob1.y - ob2.y);
  }
  public static Vector2 operator * (Vector2 ob, decimal scalar)
  {
    return new Vector2 (ob.x * scalar, ob.y * scalar);
  }
  public static Vector2 operator * (decimal scalar, Vector2 ob)
  {
    return new Vector2 (ob.x * scalar, ob.y * scalar);
  }

  public decimal Length()//ベクトルの長さ
  {
    return x * x + y * y;
  }
  public static decimal DotProduct(Vector2 ob1, Vector2 ob2)//内積
  {
    return ob1.x * ob2.x + ob1.y * ob2.y;
  }
  public static decimal CrossProduct(Vector2 ob1, Vector2 ob2)//外積。第2引数が反時計回り側で正。
  {
    return ob1.x * ob2.y - ob1.y * ob2.x;
  }

  public static Vector2 Projection(Vector2 beginPoint, Vector2 endPoint, Vector2 point)//点の射影
  {
    Vector2 segment = endPoint - beginPoint;
    decimal ratio = Vector2.DotProduct(point - beginPoint, segment) / segment.Length();
    return beginPoint + segment * ratio;//始点にたす
  }

public static long WhereVector(Vector2 beginPoint, Vector2 endPoint, Vector2 point)
  {//ベクトルに対する点の位置
    Vector2 segment = endPoint - beginPoint;
    Vector2 aimVec = point - beginPoint;
    if(Vector2.CrossProduct(segment, aimVec) > EPS)
      return 1;//反時計回り側
    else if(Vector2.CrossProduct(segment, aimVec) < -EPS)
      return 2;//時計回り側
    else if(Vector2.DotProduct(segment, aimVec) < -1+EPS)
      return 3;//ベクトル反対向きの側
    else if(segment.Length() < aimVec.Length())
      return 4;//ベクトル向きの側
    else
      return 5;//ベクトル上
  }

  public static Vector2 IntersectPoint(Vector2 vecA, Vector2 vecB, 
    Vector2 vecAsub, Vector2 vecBsub)//2線分の交点
  {
    Vector2 leftPoint = Vector2.Projection(vecA, vecB, vecAsub);//線分左端点の射影
    Vector2 rightPoint = Vector2.Projection(vecA, vecB, vecBsub);//線分右端点の射影
    decimal leftLength = (vecAsub - leftPoint).Length();
    decimal rightLength = (vecBsub - rightPoint).Length();

    leftLength = (decimal)(Math.Sqrt((double)leftLength));
    rightLength = (decimal)(Math.Sqrt((double)rightLength));
    
    if(leftLength < EPS) return leftPoint;
    else if(rightLength < EPS) return rightPoint;
    decimal ratio = leftLength / (leftLength + rightLength);
    return (leftPoint + ratio * (rightPoint - leftPoint));
  }
  
}