Reflection Invariance

1st Reflection Set

2nd to 8th Reflection Sets

Final Image Point ONLY

Move A to A' (Use Arrow Keys with <SHIFT> when close)

D = (29.444160780258553, 29.275658048235623)
C = (87.21608150381896, 4.920828723597406)
e = Line(C, D)
B = (120.63317290274115, 30.97483218716387)
f = Line(B, e)
d = Line(C, B)
g = Line(D, d)
A' = Intersect(f, g)
R = (-35.12445649901476, 74.02057704001282)
A = (44.736728030612774, 64.95831496572882)
R' = Mirror(R, A)
R'' = Mirror(R', B)
R''' = Mirror(R'', C)
E = Mirror(R''', D)
E' = Mirror(E, A)
E'' = Mirror(E', B)
E''' = Mirror(E'', C)
F = Mirror(E''', D)
F' = Mirror(F, A)
F'' = Mirror(F', B)
F''' = Mirror(F'', C)
G = Mirror(F''', D)
G' = Mirror(G, A)
G'' = Mirror(G', B)
G''' = Mirror(G'', C)
H = Mirror(G''', D)
H' = Mirror(H, A)
H'' = Mirror(H', B)
H''' = Mirror(H'', C)
I = Mirror(H''', D)
I' = Mirror(I, A)
I'' = Mirror(I', B)
I''' = Mirror(I'', C)
J = Mirror(I''', D)
J' = Mirror(J, A)
J'' = Mirror(J', B)
J''' = Mirror(J'', C)
K = Mirror(J''', D)
K' = Mirror(K, A)
K'' = Mirror(K', B)
K''' = Mirror(K'', C)
L = Mirror(K''', D)
L' = Mirror(L, A)
u = Vector(R, R')
v = Vector(R', R'')
M = Point(v)
w = Vector(M, R''')
N = Point(w)
z = Vector(N, E)
a = false
c = false
b = false
h = false
DistRL = Distance(R, L)
poly1, d_1, c_1, b_1, a_1 = Polygon(D, C, B, A)

Tool: Complex Multiplication (command ComplexMultiplication)
Select Points at O(0, 0), P(0, -1), A and B for A*B
Input: O, P, A, B
Output: j, AB

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
b = Segment(O, A)
f = Segment(O, B)
G = Intersect(d, xAxis, 1)
g = Circle(D, P, G)
E = Intersect(g, yAxis, 2)
e = Circle(O, E)
a, h = AngularBisector(f, b)
D' = Mirror(D, a)
i = Ray(O, D')
AB = Intersect(e, i, 1)
j = Segment(O, AB)

Tool: Complex Division (command ComplexDivision)
Select Points O(0, 0), P(0, -1), A and B for A/B
Input: O, P, A, B
Output: l, C

A/B

c = Circle(O, A)
d = Circle(O, B)
D = Intersect(c, xAxis, 2)
e = AngularBisector(A, O, D)
B' = Mirror(B, e)
f = Ray(O, B')
E = Intersect(c, yAxis, 1)
F = Intersect(d, xAxis, 1)
g = Segment(F, E)
G = Midpoint(g)
h = OrthogonalLine(G, g)
i = Segment(P, F)
H = Midpoint(i)
j = OrthogonalLine(H, i)
I = Intersect(h, j)
k = Circle(I, F)
J = Intersect(k, xAxis, 2)
p = Circle(O, J)
C = Intersect(p, f)
l = Segment(O, C)

Tool: Complex Addition (command ComplexAddition)
Select Points O(0, 0), A and B for A + B
Input: O, A, B
Output: C', c

A + B

u = Vector(O, B)
C' = Translate(A, u)
c = Segment(O, C')

Tool: Complex Subtraction (command ComplexSubtraction)
Select Points O(0, 0), A and B for A - B
Input: O, A, B
Output: c, A'

A - B

u = Vector(B, O)
A'_1 = Translate(A, u)
A' = Translate(A, u)
c = Segment(O, A')