Problem:
Projection

For given three points p1, p2, p, find the projection point x of p onto p1p2.

Input

xp1 yp1 xp2 yp2
q
xp0 yp0
xp1 yp1
...
xpq−1 ypq−1

In the first line, integer coordinates of p1 and p2 are given. Then, q queries are given for integer coordinates of p.

Output

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

Constraints

1 ≤ q ≤ 1000

-10000 ≤ xi, yi ≤ 10000

p1 and p2 are not identical.

Sample Input 1

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

Sample Output 1

-1.0000000000 0.0000000000
0.0000000000 0.0000000000
1.0000000000 0.0000000000

Sample Input 2

0 0 3 4
1
2 5

Sample Output 2

3.1200000000 4.1600000000

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()
	{
		string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
		Vector2 beginPoint = new Vector2(decimal.Parse(input[0]), decimal.Parse(input[1]));
    Vector2 endPoint = new Vector2(decimal.Parse(input[2]), decimal.Parse(input[3]));
		long q = long.Parse(Console.ReadLine());

    for(long i = 0; i < q; i++)
    {
      string[] inputSub = Console.ReadLine().Split(' ');
      Vector2 answer = Vector2.Projection(beginPoint, endPoint,
        new Vector2(decimal.Parse(inputSub[0]), decimal.Parse(inputSub[1])));
      Console.WriteLine(answer.x + " " + answer.y);
    }
	}
}

class Vector2//2次元ベクトル
{
  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 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 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
  }
}