Problem:
Reflection

For given three points p1, p2, p, find the reflection 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 reflection 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 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000

Sample Input 2

0 0 3 4
3
2 5
1 4
0 3

Sample Output 2

4.2400000000 3.3200000000
3.5600000000 2.0800000000
2.8800000000 0.8400000000

Solution in Scala (judge verdict: Accepted)

import scala.io.StdIn.{readLine,readInt}

object Main {
  def main(args: Array[String]) = {
    val l = readLine().split(" ").map(_.toDouble)
    val (vx, vy) = (l(2)-l(0), l(3)-l(1))
    val n = readInt()
    val sqr = vx*vx + vy*vy
    val (vsqxx, vsqxy, vsqyy) = (2*(vx*vx)/sqr,2*(vy*vx)/sqr, 2*(vy*vy)/sqr)

    val str = new StringBuilder
    for( i <- 1 to n ) {
      val l2 = readLine().split(" ").map(_.toDouble)
      val (vx2, vy2) = (l2(0)-l(0),l2(1)-l(1))
      val (xt, yt) = ( vsqxx*vx2 + vsqxy*vy2 + 2*l(0)-l2(0), vsqxy*vx2 + vsqyy*vy2 + 2*l(1)-l2(1) )

      str ++= xt + " "+ yt + "\n"
    }
    print(str.toString)
  }
}