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&minus;1 ypq&minus;1

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

Output

xt0 yt0
xt1 yt1
...
xtq-1 ytq-1

-->

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



Sample input:
0 0 2 0
3
-1 1
0 1
1 1


Sample output:
-1.0000000000 -1.0000000000
0.0000000000 -1.0000000000
1.0000000000 -1.0000000000

Submission status: Accepted

Solution code:

import math
EPS=1e-10

#点类
class Point():

    def __init__(self,x,y):
        self.x=x
        self.y=y
    
    def __sub__(self,p):
        return Point(self.x - p.x, self.y - p.y);
    def __add__(self,p):
        return Point(self.x + p.x, self.y + p.y)
           
    def __mul__(self,a): #a: scalar
        return Point(self.x * a, self.y * a)
    def __truediv__(self,a): #a: scalar
        return Point(self.x / a, self.y / a)
   
    def __str__(self):
       return  str(self.x)+','+str(self.y)
    def __repr__(self):
        return  'Point('+str(self.x)+','+str(self.y)+')'
    
    def __lt__(self, other):    
        if self.y-other.y==0:
            return self.x<other.x
        else:
            return self.y<other.y
            
    def __eq__(self, other):    
        return abs(self.x-other.x)<EPS and  abs(self.y-other.y)<EPS


# 线段类
class Segment():
    def __init__(self,p1, p2):
        self.p1=p1
        self.p2=p2
    def __str__(self):
        return  'segment:('+str(self.p1)+';'+str(self.p2)+')'
    def __repr__(self):
        return  'segment:('+str(self.p1)+';'+str(self.p2)+')'


class Circle():
    def __init__(self,c, r):
        self.c=c
        self.r=r

    def __str__(self):
       return  'Circle:(center point: '+str(self.c)+'; radius: '+str(self.r)+')'
    def __repr__(self):
       return  'Circle:(center point: '+str(self.c)+'; radius: '+str(self.r)+')'
   
    
#定义多边形
class Polygon():
    def __init__(self,ps=[]):
        self.ps=ps
        self.size=len(ps)
  
    def __getitem__(self, i):#iter override 
        return self.ps[i]  
    def __setitem__(self,i,p): 
        self.ps[i]=p               
    def __iter__(self):     
        return self.ps  
    
    def addpoint(self,i,p):
        self.ps.insert(i,p)
        self.size+=1
    def delpoint(self,i):
        self.size-=1
        return self.ps.pop(i)
    def sortYX(self):
        self.ps.sort()
        #self.ps.sort(key=attrgetter('y','x'))
    def __str__(self):
       return  'Polygon:'+str(tuple(self.ps))
    def __repr__(self):
       return  'Polygon:'+str(tuple(self.ps))
        
    def __len__(self):
        return len(self.ps)
    def __eq__(self, other):  
         return self.ps==other.ps
    
    def draw(self):
      
       turtle.screensize(800,800,"black")
       #turtle.setup(width=0.9,height=0.9)
       turtle.title("Polygon convex hull")
       turtle.setworldcoordinates(-400,-400,400,400) 

       #print(turtle.screensize())
       #mywin = turtle.Screen()    
       #mywin.   
       t=turtle.Turtle() 
       #mywin=turtle.Screen()
       
       t.pencolor("red")
       for pt in self.ps:
           t.goto(pt.x,pt.y)
           t.dot(10,'white')
       
 

#***************************点、向量****************************

#向量的模的平方
def norm(p):  
    return p.x * p.x + p.y * p.y


#向量P的长度
def length(p):
    return math.sqrt(p.x * p.x + p.y * p.y)


# 向量的(点)内积, dot(a,b)=|a|*|b|*cos(a,b) (从a,到b的角)
# =============================================================================
# r=dot(a,b),得到矢量a和b的点积，如果两个矢量都非零矢量  
# r<0：两矢量夹角为钝角； 
# r=0：两矢量夹角为直角； 
# r>0：两矢量夹角为锐角  
# =============================================================================
def dot(a, b) :
    return a.x * b.x + a.y * b.y



# =============================================================================
# # 向量的（叉）外积 cross(a,b)=|a||b|*sin(a,b) (从a,到b的角)由a,b构成的平行四边的面积
# r=cross(a,b),得到向量a和向量b的叉积  
# r>0：b在矢量a的逆时针方向；  
# r=0：a,b 平行共线；  
# r<0：b在向量a的顺时针方向 
# =============================================================================
def cross( a, b) :
    return a.x * b.y - a.y * b.x

# 点p在线段s上的投影
def project(s, p):
    base = s.p2 - s.p1
    r = dot(p - s.p1, base) / norm(base)
    return s.p1 + base * r 


# 点a到点b的距离
def getDistance(a, b) :
    return length(a - b)

# 线段l和点p的距离
def getDistanceLP(l, p) :
    return abs( cross(l.p2 - l.p1, p - l.p1) / length(l.p2 - l.p1) )

#getDistanceLP(s3, p7)
    
#线段s与点p的距离
def getDistanceSP(s, p) :
    if (dot(s.p2 - s.p1, p - s.p1) < 0.0):
        return length(p - s.p1)
    if (dot(s.p1 - s.p2, p - s.p2) < 0.0):
        return length(p - s.p2)
    return getDistanceLP(s, p)

#print(getDistanceLP(s3, Point(5,5)))
#print(getDistanceSP(s3, Point(5,5)))


#*************************线段********************************/
# 线段s1，s2是否正交 <==> 内积为0
def isOrthogonalSG(s1, s2) :
    return abs(dot(s1.p2 - s1.p1, s2.p2 - s2.p1))<EPS


# 线段s1，s2是否平行 <==> 叉积为0
def isParallelLN(s1,s2) :
    return abs(cross(s1.p2 - s1.p1, s2.p2 - s2.p1))<0




# 逆时针方向ccw（Counter-Clockwise）
COUNTER_CLOCKWISE = 1;
CLOCKWISE = -1;
ONLINE_BACK = -2;
ONLINE_FRONT = 2;
ON_SEGMENT = 0;

def ccw(p0, p1, p2) :
    a = p1 - p0
    b = p2 - p0
    if (cross(a, b) > EPS):
        return COUNTER_CLOCKWISE
    if (cross(a, b) < -EPS):
        return CLOCKWISE
    if (dot(a, b) < -EPS):
        return ONLINE_BACK
    if (norm(a) < norm(b)):
        return ONLINE_FRONT
    
    return ON_SEGMENT;


def toleft(p0,p1,p2):
    a = p1 - p0
    b = p2 - p0  
    tmp=cross(a,b)
    if tmp > EPS:
        return 1
    elif abs(tmp)<EPS and norm(a)<=norm(b):
        return 2  #共线，p2在p0p1的右延长线上
    elif abs(tmp)<EPS and norm(a)>norm(b):
        return -2  #共线，p2在p0p1的left延长线上    
    else:
        return -1


#以线段s为对称轴与点p成线对称的点
def reflect(s, p) :
    return p + (project(s, p) - p) * 2.0


s= [int(x) for x in input().split()]
p1=Point(s[0],s[1])
p2=Point(s[2],s[3])
sg=Segment(p1,p2)
q=int(input())
for i in range(0,q):
    s= [int(x) for x in input().split()]
    p3=Point(s[0],s[1])
    pt=reflect(sg,p3)
    print(pt.x,pt.y)

Submission status: Accepted

Solution code:
from math import hypot

x1, y1, x2, y2 = map(int, input().split())
dx, dy = x2-x1, y2-y1
vector_base = hypot(dx, dy)
q = int(input())

for i in range(q):
    x3, y3 = map(int, input().split()) 
    r = ((x3-x1)*dx + (y3-y1)*dy) / (vector_base**2)
    tx, ty = x1+dx*r, y1+dy*r
    print('{:.08f}'.format(x3+2*(tx-x3)), '{:.08f}'.format(y3+2*(ty-y3)))

Submission status: Accepted

Solution code:
from math import sin, cos, atan2

def sgn(x, eps=1e-10):
    if x < -eps: return -1
    if -eps <= x <= eps: return 0
    if eps < x: return 1

class Vector():
    def __init__(self, x=0.0, y=0.0):
        self.x = x
        self.y = y

    def arg(self):
        return atan2(self.y, self.x)

    def norm(self):
        return (self.x**2 + self.y**2)**0.5

    def rotate(self, t):
        nx = self.x * cos(t) - self.y * sin(t)
        ny = self.x * sin(t) + self.y * cos(t)
        return Vector(nx, ny)

    def counter(self):
        nx = -self.x
        ny = -self.y
        return Vector(nx, ny)

    def times(self, k):
        nx = self.x * k
        ny = self.y * k
        return Vector(nx, ny)

    def unit(self):
        norm = self.norm()
        nx = self.x / norm
        ny = self.y / norm
        return Vector(nx, ny)

    def normal(self):
        norm = self.norm()
        nx = -self.y / norm
        ny = self.x / norm
        return Vector(nx, ny)

    def add(self, other): #Vector, Vector -> Vector
        nx = self.x + other.x
        ny = self.y + other.y
        return Vector(nx, ny)

    def sub(self, other):
        nx = self.x - other.x
        ny = self.y - other.y
        return Vector(nx, ny)

    def dot(self, other): #Vector, Vector -> int
        return self.x * other.x + self.y * other.y

    def cross(self, other): #Vector, Vector -> int
        return self.x * other.y - self.y * other.x

    def __str__(self):
        return '{:.9f}'.format(self.x) + ' ' + '{:.9f}'.format(self.y)

class Line():
    def __init__(self, bgn=Vector(), end=Vector()):
        self.bgn = bgn
        self.end = end

    def build(self, a, b, c): #ax + by == 1
        assert sgn(a) != 0 or sgn(b) != 0
        if sgn(b) == 0:
            self.bgn = Vector(-c / a, 0.0)
            self.end = Vector(-c / a, 1.0)
        else:
            self.v = Vector(0, -c / b)
            self.u = Vector(1.0, -(a + b) / b)

    def vec(self):
        return self.end.sub(self.bgn)

    def projection(self, point):
        v = self.vec()
        u = point.sub(self.bgn)
        k = v.dot(u) / v.norm()
        h = v.unit().times(k)
        return self.bgn.add(h)

    def refrection(self, point):
        proj = self.projection(point)
        return proj.sub(point).times(2).add(point)

xp1, yp1, xp2, yp2 = map(int, input().split())
q = int(input())

p1 = Vector(xp1, yp1)
p2 = Vector(xp2, yp2)
l = Line(p1, p2)

for _ in range(q):
    x, y = map(int, input().split())
    p = Vector(x, y)
    ref = l.refrection(p)
    print(ref)

Submission status: Accepted

Solution code:
import math

class Vector:
    def __init__(self,x,y):
        self.x = x
        self.y = y
        
    def norm_2(self):
        return dot(self,self)
    
    def norm(self):
        return math.sqrt(self.norm_2())
    
def v_sum(v1,v2):
    return Vector(v1.x+v2.x,v1.y+v2.y) 
def scalar_multi(k,v):
    return Vector(k*v.x,k*v.y)
def v_diff(v1,v2):
    return v_sum(v1,scalar_multi(-1,v2))
    
def dot(vector1,vector2):
    return vector1.x*vector2.x+vector1.y*vector2.y

def cross(vector1,vector2):
    return vector1.x*vector2.y+vector1.y*vector2.x

x1,y1,x2,y2 = map(int,input().split())
p1 = Vector(x1,y1)
p2 = Vector(x2,y2)

d = v_diff(p2,p1)

q = int(input())
for i in range(q):
    x,y = map(int,input().split())
    v = v_diff(Vector(x,y),p1)
    h = scalar_multi(dot(v,d)/d.norm_2(),d)
    w = v_sum(scalar_multi(2,v_diff(h,v)),v)
    print('{} {}'.format(v_sum(w,p1).x,v_sum(w,p1).y))

Submission status: Accepted

Solution code:
import sys
input = sys.stdin.readline


class Vector():
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, vec):
        return Vector(self.x+vec.x, self.y+vec.y)

    def __sub__(self, vec):
        return Vector(self.x-vec.x, self.y-vec.y)

    def __mul__(self, sc):
        return Vector(self.x*sc, self.y*sc)

    def __truediv__(self, sc):
        return Vector(self.x/sc, self.y/sc)

    def __iadd__(self, vec):
        self.x += vec.x
        self.y += vec.y
        return self

    def __isub__(self, vec):
        self.x -= vec.x
        self.y -= vec.y
        return self

    def __imul__(self, sc):
        self.x *= sc
        self.y *= sc
        return self

    def __itruediv__(self, sc):
        self.x /= sc
        self.y /= sc
        return self

    def __str__(self):
        return '{:.9f} {:.9f}'.format(self.x, self.y)

    def __eq__(self, vec):
        return self.x == vec.x and self.y == vec.y

    def dot(self, vec):
        return self.x * vec.x + self.y * vec.y

    def abs(self):
        return (self.x*self.x + self.y*self.y)**0.5

    def ortho(self):
        return Vector(-self.y, self.x)


x1, y1, x2, y2 = map(int, input().split())
v1 = Vector(x1, y1)
v2 = Vector(x2, y2)
n = v2-v1
n /= n.abs()
m = n.ortho()

for _ in [0]*int(input()):
    x, y = map(int, input().split())
    v = Vector(x, y) - v1
    u = v - m * v.dot(m) * 2
    print(v1 + u)

Submission status: Accepted

Solution code:
from math import sqrt
x1, y1, x2, y2 = map(int, raw_input().split())
dx = x2 - x1
dy = y2 - y1

for i in xrange(input()):
    x, y = map(int, raw_input().split())
    a = float(dx * (x - x1) + dy * (y - y1)) / (dx ** 2 + dy ** 2)
    print "%.09f %0.09f" % (2 * x1 - x + 2 * a * dx, 2 * y1 - y + 2 * a * dy)

Submission status: Accepted

Solution code:
EPS = 10**(-9)
def is_equal(a,b):
    return abs(a-b) < EPS

def norm(v,i):
    import math
    ret = 0
    n = len(v)
    for j in range(n):
        ret += abs(v[j])**i
    return math.pow(ret,1/i)

class Vector(list):
    """
    ベクトルクラス
    対応演算子
    +  : ベクトル和 
    -  : ベクトル差
    *  : スカラー倍、または内積
    ** : 外積
    += : ベクトル和
    -= : ベクトル差
    *= : スカラー倍
    /= : スカラー倍

    メソッド
    self.norm(i) : L{i}ノルムを計算
    """
    def __add__(self,other):
        n = len(self)
        ret = [0]*n
        for i in range(n):
            ret[i] = super().__getitem__(i) + other.__getitem__(i)
        return self.__class__(ret)
    
    def __radd__(self,other):
        n = len(self)
        ret = [0]*n
        for i in range(n):
            ret[i] = other.__getitem__(i) + super().__getitem__(i)
        return self.__class__(ret)
    
    def __iadd__(self, other):
        n = len(self)
        for i in range(n):
            self[i] += other.__getitem__(i)
        return self

    def __sub__(self,others):
        n = len(self) 
        ret = [0]*n
        for i in range(n):
            ret[i] = super().__getitem__(i) - others.__getitem__(i)
        return self.__class__(ret)

    def __iadd__(self, other):
        n = len(self)
        for i in range(n):
            self[i] -= other.__getitem__(i)
        return self

    def __rsub__(self,others):
        n = len(self) 
        ret = [0]*n
        for i in range(n):
            ret[i] = others.__getitem__(i) - super().__getitem__(i)
        return self.__class__(ret)
    
    def __mul__(self,other):
        n = len(self)
        if isinstance(other,list):
            ret = 0
            for i in range(n):
                ret += super().__getitem__(i)*other.__getitem__(i)
            return ret
        else:
            ret = [0]*n
            for i in range(n):
                ret[i] = super().__getitem__(i)*other
            return self.__class__(ret)

    def __rmul__(self,other):
        n = len(self)
        if isinstance(other,list):
            ret = 0
            for i in range(n):
                ret += super().__getitem__(i)*other.__getitem__(i)
            return ret
        else:
            ret = [0]*n
            for i in range(n):
                ret[i] = super().__getitem__(i)*other
            return self.__class__(ret)
    
    
    def __truediv__(self,other):
        """
        ベクトルのスカラー除法
        Vector/scalar
        """
        n = len(self)
        ret = [0]*n
        for i in range(n):
            ret[i] = super().__getitem__(i)/other
        return self.__class__(ret)
    
    def norm(self,i):
        """
        L{i}ノルム
        self.norm(i)
        """
        return norm(self,i)
    
    def __pow__(self,other):
        """
        外積
        self**other
        """
        n = len(self)
        ret = [0]*3
        x = self[:]
        y = other[:]
        if n == 2:
            x.append(0)
            y.append(0)
        if n == 2 or n == 3:
            for i in range(3):
                ret[0],ret[1],ret[2] = x[1]*y[2]-x[2]*y[1],x[2]*y[0]-x[0]*y[2],x[0]*y[1]-x[1]*y[0]
            ret = Vector(ret)
            if n == 2:
                return ret.norm(2)
            else:
                return ret

class Segment:
    """
    線分クラス
    """
    def __init__(self,v1,v2):
        self.v1 = v1
        self.v2 = v2

class Line(Segment):
    """
    直線クラス
    """
    def get_unit_vec(self):
        return (self.v2-self.v1)/norm(self.v2-self.v1,2)
    
    def projection(self,vector):
        unit_vec = self.get_unit_vec()
        t = unit_vec*(vector-self.v1)
        return self.v1 + t*unit_vec
    
    def is_vertical(self,other):
        return is_equal(0,self.get_unit_vec()*other.get_unit_vec())
    
    def is_horizontal(self,other):
        return is_equal(0,self.get_unit_vec()**other.get_unit_vec())
    
    def reflection(self,vector):
        projection = self.projection(vector)
        v = projection - vector
        return projection + v


xp1,yp1,xp2,yp2 = map(float,input().split())
q = int(input())
ps = [list(map(int,input().split())) for i in range(q)]

p1 = Vector([xp1,yp1])
p2 = Vector([xp2,yp2])
L = Line(p1,p2)

for p in ps:
    ans = L.reflection(p)
    ans = [float(round(a,11)) for a in ans]
    print(*ans)

Submission status: Accepted

Solution code:
x1,y1,x2,y2=map(int,input().split())
p1,p2=complex(x1,y1),complex(x2,y2)
a=p2-p1
dis=(x1-x2)**2+(y1-y2)**2
for i in range(int(input())):
    p=complex(*map(int,input().split()))
    b=p-p1
    co=(a.real*b.real+a.imag*b.imag)/dis
    ans=p+2*(co*a-b)
    print(ans.real,ans.imag)

Submission status: Accepted

Solution code:
class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y
    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)
    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)
    def __mul__(self, other):
        return Point(self.x * other, self.y * other)
    def __floordiv__(self, other):
        return Point(self.x / other, self.y / other)
    def __repr__(self):
        return str(self.x) + ' ' + str(self.y)

class Vector(Point):
    pass

class Segment:
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2

def points_to_vector(p1, p2):
    x = p1.x - p2.x
    y = p1.y - p2.y
    return Vector(x, y)

def vector(p):
    return Vector(p.x, p.y)

def dot(v1, v2):
    return v1.x * v2.x + v1.y * v2.y

def cross(v1, v2):
    return v1.x * v2.y - v1.y * v2.x

def norm(v):
    return v.x**2 + v.y**2

def project(s, p):
    base = points_to_vector(s.p1, s.p2)
    hypo = points_to_vector(p, s.p1)
    r = dot(hypo, base) / norm(base)
    return s.p1 + base * r

def reflect(s, p):
    return p + (project(s, p) -p) * 2

import sys
# sys.stdin = open('input.txt')

s = list(map(int, input().split()))
p1 = Point(s[0], s[1])
p2 = Point(s[2], s[3])
segment = Segment(p1, p2)

q = int(input())
for i in range(q):
    x, y = map(int, input().split())
    p = Point(x, y)
    ans = reflect(segment, p)
    print(ans)

Submission status: Accepted

Solution code:
import math

class Point:
    def __init__(self,x,y):
        self.x = x
        self.y = y

    def __add__(self,a):
        return self.__class__(self.x+a.x,self.y+a.y)

    def __sub__(self,a):
        return self.__class__(self.x-a.x,self.y-a.y)

    def __mul__(self,d):
        return self.__class__(self.x*d,self.y*d)

    def __truediv__(self,d):
        return self.__class__(self.x/d,self.y/d)

    def __str__(self):
        return '%.10f %.10f'%(self.x,self.y)

    def abs(self):
        return self.norm()**(1.0/2.0)

    def norm(self):
        return (self.x*self.x+self.y*self.y)

    def rotate(self,d):
        r = math.pi*d/180.0
        return self.__class__( self.x*math.cos(r)-self.y*math.sin(r),
                               self.x*math.sin(r)+self.y*math.cos(r))

    def dot(self,p):
        return (self.x*p.x+self.y*p.y)

class Segment:
    def __init__(self,p1,p2):
        self.p1 = p1
        self.p2 = p2

def project(s,p):
    v = s.p2-s.p1
    r = v.dot(p-s.p1)/v.norm()
    return s.p1+v*r

def reflect(s,p):
    return p+(project(s,p)-p)*2.0

def main():
    a,b,c,d = map(float,input().split())
    s = Segment(Point(a,b),Point(c,d))
    q = int(input())
    for _ in range(q):
        e,f = map(float,input().split())
        p = Point(e,f)
        print (reflect(s,p))


if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
a,b,c,d = map(float,input().split())
a = complex(a,b)
b = complex(c,d)
for _ in range(int(input())):
    c = complex(*map(float,input().split()))
    q = b-a
    c-=a
    p = a+ q*((c/q).conjugate())
    print(p.real,p.imag)

Submission status: Accepted

Solution code:
def reflection(line, point):
    x0, y0, x1, y1 = line
    p, q = point
    x1 -= x0; y1 -= y0
    p -= x0; q -= y0
    cv = p*x1 + q*y1
    sv = p*y1 - q*x1
    cv2 = cv**2 - sv**2
    sv2 = 2*cv*sv
    dd = (p**2 + q**2)*(x1**2 + y1**2)
    if dd == 0:
        return x0 + p, y0 + q
    return x0 + (cv2 * p - sv2 * q) / dd, y0 + (sv2 * p + cv2 * q) / dd

def solve():
    x0, y0, x1, y1 = map(int, input().split())
    q = int(input())
    for i in range(q):
        x, y = map(int, input().split())
        print("%.16f %.16f" % reflection((x0, y0, x1, y1), (x, y)))
solve()

Submission status: Accepted

Solution code:
import math

EPS = 1e-10

class Segment():
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2

class Point():
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, point):
        # + 演算子での挙動を指定
        return Point(self.x+point.x, self.y+point.y)

    def __sub__(self, point):
        # - 演算子での挙動を指定
        return Point(self.x-point.x, self.y-point.y)

    def __mul__(self, a):
        # * 演算子での挙動を指定
        return Point(a*self.x, a*self.y)

    def __truediv__(self, a):
        # / 演算子での挙動を指定
        return Point(self.x/a, self.y/a)

    def __abs__(self):
        # abs関数での挙動を指定
        return math.sqrt(self.norm())

    def norm(self):
        return self.x**2+self.y**2

    def __eq__(self, point):
        # == 演算子での挙動を指定
        return abs(self.x-point.x) < EPS and abs(self.y-point.y) <EPS

def dot(a, b):
    return a.x*b.x+a.y*b.y

def cross(a, b):
    return a.x*b.y - a.y*b.x

def isOrthogonal(a, b):
    return dot(a, b) == 0

def isParallel(a, b):
    return cross(a, b) == 0

def project(s, p):
    #s: Segment(), p: Point()
    base = s.p2 - s.p1
    r = dot(p-s.p1, base)/base.norm()
    return s.p1+base*r

def reflect(s, p):
    return p+(project(s, p)-p)*2

if __name__ == '__main__':
    from sys import stdin
    input = stdin.readline

    x1, y1, x2, y2 = map(int, input().split())
    s = Segment(Point(x1, y1), Point(x2, y2))

    q = int(input())
    for _ in range(q):
        x0, y0 = map(int, input().split())
        p = Point(x0, y0)
        reflection = reflect(s, p)
        print(reflection.x, reflection.y)

Submission status: Accepted

Solution code:
from math import pi, cos, sin, atan2
EPS = 10**(-9)

def eq(value1, value2):
    return abs(value1-value2) <= EPS

class Point():
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.arg = atan2(y, x) # -PI ~ PI
    
    def __str__(self):
        return "{0:.8f} {1:.8f}".format(self.x, self.y)
    
    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)
    
    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)
    
    def __mul__(self, scal):
        return Point(self.x*scal, self.y*scal)
    
    def __truediv__(self, scal):
        return Point(self.x/scal, self.y/scal)
    
    def __eq__(self, other):
        return eq(self.x, other.x) and eq(self.y, other.y)

    # 原点からの距離
    def __abs__(self):
        return (self.x**2+self.y**2)**0.5
    
# 原点を中心にrad角だけ回転した点
def Rotation(vec: Point, rad):
    return Point(vec.x*cos(rad)-vec.y*sin(rad), vec.x*sin(rad)+vec.y*cos(rad))


class Circle():
    def __init__(self, p, r):
        self.p = p
        self.r = r


class Line():
    # 点a, bを通る
    def __init__(self, a, b):
        self.a = a
        self.b = b
        self.arg = (a-b).arg % pi
    
    def __str__(self):
        return "[({0}, {1}) - ({2}, {3})]".format(self.a.x, self.a.y, self.b.x, self.b.y)

    # pointを通って平行
    def par(self, point):
        return Line(point, point+(self.a-self.b))

    # pointを通って垂直
    def tan(self, point):
        return Line(point, point + Rotation(self.a-self.b, pi/2))


class Segment(Line):
    def __init__(self, a, b):
        super(Line, self).__init__(a, b)


# 符号付き面積
def cross(vec1: Point, vec2: Point):
    return vec1.x*vec2.y - vec1.y*vec2.x

# 内積
def dot(vec1: Point, vec2: Point):
    return vec1.x*vec2.x + vec1.y*vec2.y

# 点a->b->cの回転方向
def ccw(a, b, c):
    if cross(b-a, c-a) > EPS: return +1 # COUNTER_CLOCKWISE
    if cross(b-a, c-a) < -EPS: return -1 # CLOCKWISE
    if dot(c-a, b-a) < -EPS: return +2 # c -> a -> b
    if abs(b-a) < abs(c-a): return -2 # a -> b -> c
    return 0 # a -> c -> b


# pのlへの射影
def projection(l, p):
    t = dot(l.b-l.a, p-l.a) / abs(l.a-l.b)**2
    return l.a + (l.b-l.a)*t

# pのlによる反射
def reflection(l, p):
    return p + (projection(l, p) - p)*2

def isPararell(l1, l2):
    return eq(cross(l1.a-l1.b, l2.a-l2.b), 0)

def isVertical(l1, l2):
    return eq(dot(l1.a-l1.b, l2.a-l2.b), 0)


def isIntersect_lp(l, p):
    return abs(ccw(l.a, l.b, p)) != 1

def isIntersect_ll(l1, l2):
    return not isPararell(l1, l2) or isIntersect_lp(l1, l2.a)

def isIntersect_sp(s, p):
    return ccw(s.a, s.b, p) == 0

def isIntersect_ss(s1, s2):
    return ccw(s1.a, s1.b, s2.a)*ccw(s1.a, s1.b, s2.b) <= 0 and ccw(s2.a, s2.b, s1.a)*ccw(s2.a, s2.b, s1.b) <= 0

def isIntersect_ls(l, s):
    return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS

def isIntersect_cp(c, p):
    return abs(abs(c.p - p) - c.r) < EPS

def isIntersect_cl(c, l):
    return distance_lp(l, c.p) <= c.r + EPS

def isIntersect_cs(c, s):
    pass

def isIntersect_cc(c1, c2):
    pass


def distance_pp(p1, p2):
    return abs(p1-p2)

def distance_lp(l, p):
    return abs(projection(l,p)-p)

def distance_ll(l1, l2):
    return 0 if isIntersect_ll(l1, l2) else distance_lp(l1, l2.a)

def distance_sp(s, p):
    r = projection(s, p)
    if isIntersect_sp(s, r): return abs(r-p)
    return min(abs(s.a-p), abs(s.b-p))

def distance_ss(s1, s2):
    if isIntersect_ss(s1, s2): return 0
    return min([distance_sp(s1, s2.a), distance_sp(s1, s2.b), distance_sp(s2, s1.a), distance_sp(s2, s1.b)])

def distance_ls(l, s):
    if isIntersect_ls(l, s): return 0
    return min(distance_lp(l, s.a), distance_lp(l, s.b))


def crosspoint_ll(l1, l2):
    A = cross(l1.b - l1.a, l2.b - l2.a)
    B = cross(l1.b - l1.a, l1.b - l2.a)
    if eq(abs(A), 0) and eq(abs(B), 0): return l2.a
    return l2.a + (l2.b - l2.a) * B / A

def crosspoint_ss(s1, s2):
    return crosspoint_ll(s1, s2)

def crosspoint_lc(l, c):
    if eq(distance_lp(l, c.p), c.r): return [c.p]
    p = projection(l, c.p)
    e = (l.b - l.a) / abs(l.b-l.a)
    dis = (c.r**2-abs(p-c.p)**2)**0.5
    return [p + e*dis, p - e*dis]

def crosspoint_sc(s, c):
    pass

def crosspoint_cc(c1, c2):
    d = abs(c1.p-c2.p)
    if not abs(c1.r-c2.r) <= d <= c1.r+c2.r:
        return []
    mid_p = (c2.p * (c1.r**2-c2.r**2+d**2) + c1.p * (c2.r**2-c1.r**2+d**2)) / (2*d**2)
    tanvec = Rotation(c1.p-c2.p, pi/2)
    return crosspoint_lc(Line(mid_p, mid_p+tanvec), c1)


# pからのcの接点
def tangent_cp(c, p):
    return crosspoint_cc(c, Circle(p, (abs(p-c.p)**2 - c.r**2)**0.5))





import sys
input = sys.stdin.readline

def verify_1A():
    p1x, p1y, p2x, p2y = map(int, input().split())
    l = Line(Point(p1x, p1y), Point(p2x, p2y))
    Q = int(input())
    Query = [list(map(int, input().split())) for _ in range(Q)]
    for px, py in Query:
        p = Point(px, py)
        print(projection(l, p))

def verify_1B():
    p1x, p1y, p2x, p2y = map(int, input().split())
    l = Line(Point(p1x, p1y), Point(p2x, p2y))
    Q = int(input())
    Query = [list(map(int, input().split())) for _ in range(Q)]
    for px, py in Query:
        p = Point(px, py)
        print(reflection(l, p))

verify_1B()

Submission status: Accepted

Solution code:
def project(x,y):
    base=[x2-x1,y2-y1]
    hypo=[x-x1,y-y1]
    r=(base[0]*hypo[0]+base[1]*hypo[1])/(base[0]**2+base[1]**2)
    return x1+base[0]*r,y1+base[1]*r


def reflect(x,y):
    px,py=project(x,y)
    return x+(px-x)*2,y+(py-y)*2


x1,y1,x2,y2=map(int,input().split())
q=int(input())
for i in range(q):
    x,y=map(int,input().split())
    print(*reflect(x,y))

Submission status: Accepted

Solution code:
def dot(a,b):
    return a.real*b.real+a.imag*b.imag

x1, y1, x2, y2 = map(int, input().split())
p1=x1+y1*1j
p2=x2+y2*1j
l=p2-p1
l_norm=dot(l,l)         #lの大きさの２乗を計算
q=int(input())

for x3, y3 in (map(int, input().split()) for _ in [0]*q):
    p3=x3+y3*1j
    a=p3-p1
    k=dot(a,l)/l_norm
    projection_vector=k*l
    reflect_vector=projection_vector-a
    print(x3+2*reflect_vector.real,y3+2*reflect_vector.imag)

Submission status: Accepted

Solution code:
EPS = 0.0000000001

class Point:
    
    global EPS
    
    def __init__(self, x = 0, y = 0):
        self.x = x
        self.y = y
        
        
    def __add__(a, b):
        s = a.x + b.x
        t = a.y + b.y
        return Point(s, t)
        
    def __sub__(a, b):
        s = a.x - b.x
        t = a.y - b.y
        return Point(s, t)
            
    def __mul__(self, a):
        s = a * self.x
        t = a * self.y
        return Point(s, t)
        
    def __truediv__(self, a):
        s = self.x / a
        t = self.y / a
        return Point(s, t)
            
            
            
            
    def norm(self):
        return self.x * self.x + self.y * self.y
        
    def abs(self):
        return self.norm() ** 0.5
            
    
            
            
    def __eq__(self, other):
        return abs(self.x - other.y) < self.EPS and abs(self.y - other.y) < self.EPS
            
            
            
    def dot(self, b):
        return self.x * b.x + self.y * b.y
        
    def cross(self, b):
        return self.x * b.y - self.y * b.x
    
    
class Segment:
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2

def project(s, p):
    base = s.p2 - s.p1
    hypo = p - s.p1
    r = hypo.dot(base) / base.norm()
    return s.p1 + base * r

def reflecton(s, p):
    return p + (project(s,p) - p) * 2


nums=list(map(int,input().split()))
s = Segment(Point(nums[0], nums[1]), Point(nums[2], nums[3]))

n = int(input())
for i in range(n):
    nums=list(map(int,input().split()))
    p = Point(nums[0], nums[1])
    x = reflecton(s, p)
    print(x.x, x.y)