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 JAVA (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.math.BigInteger;
 
public class Main implements Runnable {
	
	//static int mod = 1000000007;
	
    public static void main(String[] args) {
    	new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
    }
    
    public void run() {
        FastScanner sc = new FastScanner();
        
        int q = sc.nextInt();

        for(int i=0;i<q;i++){
        	Point p0 = new Point(sc.nextDouble(),sc.nextDouble());
        	Point p1 = new Point(sc.nextDouble(),sc.nextDouble());
        	Point p2 = new Point(sc.nextDouble(),sc.nextDouble());
        	Point p3 = new Point(sc.nextDouble(),sc.nextDouble());
        	Line l1 = new Line(p0,p1);
        	Line l2 = new Line(p2,p3);
        	Point c = l1.crossPoint(l2);
        	System.out.println(c.x + " " + c.y);
        }
    }

    
}

class Line {
	static final double allowableError = 0.00000001;
	double a;
	double b;
	double c;
	
	//2点p,qを通る直線
	public Line(Point p, Point q){
		if(p.y == q.y){
			this.a = 0;
			this.b = 1;
			this.c = -(p.y);
		}
		else if(p.x == q.x){
			this.a = 1;
			this.b = 0;
			this.c = -(p.x);
		}
		else{
			this.a = p.y - q.y;
			this.b = q.x - p.x;
			this.c = - a*p.x - b*p.y;
		}
	}
	//ax+by+c=0
	public Line(double a, double b, double c){
		this.a = a;
		this.b = b;
		this.c = c;
	}
	//y=ax+c
	public Line(double a, double c){
		this.a = a;
		this.b = -1;
		this.c = c;
	}
	
	//点pからの垂線の足
	public Point projection(Point p){
		//-bx+ay+d=0がこの直線と垂直でpを通る直線とし、dを求める
		double d = b*p.x - a*p.y;
		return crossPoint(new Line(-b,a,d));
	}
	
	//点pと線対称な点
	public Point reflection(Point p){
		Point proj = projection(p);
		double x = proj.x + (proj.x - p.x);
		double y = proj.y + (proj.y - p.y);
		return new Point(x,y);
	}
	
	//直線lとの交点
	public Point crossPoint(Line l){
		if(a==0){ //b=1前提
			double x = (l.b*c - l.c)/l.a;
			return new Point(x,-c);
		}
		if(l.a==0){ //l.b=1前提
			double x = (b*l.c - c)/a;
			return new Point(x, -l.c);
		}
		
		//xの係数をlと等しくする
		//気持ちは double A = l.a;
		double mlt = l.a/a;
		double B = b * mlt;
		double C = c * mlt;
		double y = (l.c-C)/(B-l.b);
		double x = (-b*y-c)/a;
		return new Point(x,y);
	}
	
	//直線lと平行かどうか
	boolean isParallel(Line l){
		if(Math.abs(a*l.b - l.a*b) < allowableError){
			return true;
		}
		else{
			return false;
		}
	}
	
	//直線lと垂直かどうか
	boolean isOrthogonal(Line l){
		if(Math.abs(a*l.a + b*l.b) < allowableError){
			return true;
		}
		else{
			return false;
		}
	}
	
	public void display(){
		System.out.println(a + "x + " + b + "y + " + c + " = 0");
	}
	
}

class Polygon {
	static final double allowableError = 0.00000001;
	ArrayList<Point> pl; //反時計周り
	
	public Polygon(ArrayList<Point> pol){
		this.pl = pol;
	}
	
	//面積を導出
	double area(){
		//|det|/2は作る三角形の面積に一致
		double ans = 0;
		
		for(int i=0;i<pl.size();i++){
			ans += det(pl.get(i), pl.get(next(i)));
		}
		
		return ans/2;
	}
	
	//pが多角形に含まれるなら2、pが辺上にあるなら1、pが外側にあるなら0を返す
	int contain(Point p){
		//pからx軸と平行・正方向の半直線を引き、奇数回交差すれば内部にある
		boolean isIn = false;
		for(int i=0;i<pl.size();i++){
			int upid = i;
			int downid = next(i);
			if(pl.get(i).y < pl.get(next(i)).y){
				upid = next(i);
				downid = i;
			}
			
			//ベクトルを便宜的に
			Point pup = new Point(pl.get(upid).x - p.x, pl.get(upid).y - p.y);	//p→p_i
			Point pdown = new Point(pl.get(downid).x - p.x, pl.get(downid).y - p.y); //p→p_next(i)
			
			double det = det(pup, pdown);
			if(pup.y > 0 && 0 >= pdown.y){	//2重カウントしないために不等号を>と>=にする
				if(det < 0){
					isIn = !isIn;
				}
			}
			
			//辺上判定
			if(Math.abs(det) < allowableError){	//p→p_iとp→p_next(i)が一直線上
				if(pup.x * pdown.x + pup.y * pdown.y <= 0){	//pからみて同方向でない
					return 1;
				}
			}
		}
		
		if(isIn){
			return 2;
		}
		else{
			return 0;
		}
	}
	
	//凸多角形か判定
	boolean isConvex(){
		//反時計回りに回り続けるなら凸
		for(int i=0;i<pl.size();i++){
			if(direction(pl.get(next(i)),pl.get(i),pl.get(next(next(i)))) == 1){
				return false;
			}
		}
		return true;
	}
	
	//反時計回りに1つ進んだ頂点のindex
	int next(int id){
		int size = pl.size();
		if(id<=size-2){
			return id+1;
		}
		else{
			return 0;
		}
	}
	//ベクトルのdet
	static double det(double x1, double y1, double x2, double y2){
		return x1*y2 - x2*y1;
	}
	static double det(Point p, Point q){
		return p.x*q.y - p.y*q.x;
	}
	
	//p0を起点に、p1へのベクトルからみてp2へのベクトルが反時計回りなら1、時計回りなら2
	//↑が同一直線状にあるとき、→p2が→p1と反対側なら3、→p2が→p1の延長線上なら4、→p2が→p1上にあれば5を返す
	static int direction(Point p0, Point p1, Point p2) {
		if(p0.x == p1.x) {
			if(p2.x == p0.x) {
				if((p0.y <= p2.y && p2.y <= p1.y) || (p1.y <= p2.y && p2.y <= p0.y)) {
					return 5;
				}else if (d2(p0,p2) < d2(p1,p2)) {
					return 3;
				}else {
					return 4;
				}
			}else if ((p0.y < p1.y && p2.x < p0.x) || (p0.y > p1.y && p2.x > p0.x)) {
				return 1;
			}else {
				return 2;
			}

		}else{
			//y=ax+b上にp0,p1が存在
			double a = (p1.y - p0.y) / (p1.x - p0.x);
			double b = p1.y - a * p1.x;
			if(Math.abs(p2.y - (a * p2.x + b)) < allowableError) {
				if((p0.x <= p2.x && p2.x <= p1.x) || (p1.x <= p2.x && p2.x <= p0.x)) {
					return 5;
				}else if (d2(p0,p2) < d2(p1,p2)) {
					return 3;
				}else {
					return 4;
				}
			}else if ((p0.x < p1.x && p2.y - (a * p2.x + b) > 0) || (p0.x > p1.x && p2.y - (a * p2.x + b) < 0)) {
				return 1;
			}else {
				return 2;
			}
		}
	}
	//ユークリッド距離の2乗
	static double d2(Point p1, Point p2){
		return (p2.x - p1.x) * (p2.x - p1.x) + (p2.y - p1.y) * (p2.y - p1.y);
	}

}

class Point implements Comparable<Point>{
	double x,y;
	
	public Point(double a, double b){
		this.x = a;
		this.y = b;
	}
	
	@Override
	public int hashCode() {
		final int prime = 31;
		int result = 1;
		long temp;
		temp = Double.doubleToLongBits(x);
		result = prime * result + (int) (temp ^ (temp >>> 32));
		temp = Double.doubleToLongBits(y);
		result = prime * result + (int) (temp ^ (temp >>> 32));
		return result;
	}

	@Override
	public boolean equals(Object obj) {
		if (this == obj)
			return true;
		if (obj == null)
			return false;
		if (getClass() != obj.getClass())
			return false;
		Point other = (Point) obj;
		if (Double.doubleToLongBits(x) != Double.doubleToLongBits(other.x))
			return false;
		if (Double.doubleToLongBits(y) != Double.doubleToLongBits(other.y))
			return false;
		return true;
	}
	
	@Override
	public int compareTo(Point o){
		if(x!=o.x){
			return Double.compare(x,o.x);
		}
		return Double.compare(y, o.y);
	}
		
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}
	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}
	public int[] nextIntArray(int n){
		int[] a = new int[n];
		for(int i=0;i<n;i++){
			a[i] = nextInt();
		}
		return a;
	}
	public Integer[] nextIntegerArray(int n){
		Integer[] a = new Integer[n];
		for(int i=0;i<n;i++){
			a[i] = nextInt();
		}
		return a;
	}
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}