Two Rotations Same Centre

Mirror Line 1

Mirror Line 2

C of R

Rotation Property

A = (-16.449000789880543, 7.552453408476436)
B = (-16.449000789880543, 9.80089955742311)
C = (-14.756205126018388, 9.968886913378896)
D = (-14.833737751844136, 8.922196464731305)
E = (-15.893350304796025, 9.245249072338586)
F = (-15.751207157448814, 7.410310261129232)
poly1, a, b, c, d, e, f = Polygon(A, B, C, D, E, F)
G = (-13.949045964971079, 10.247682951767036)
H = (-14.4706614136545, 6.10084013473381)
g = Segment(G, H)
I = (-12.39724000513788, 11.486519642390174)
J = (-9.045860747346874, 8.408988495157967)
h = Segment(I, J)
i = Line(H, G)
j = Line(J, I)
K = Intersect(i, j)
A' = Mirror(A, i)
B' = Mirror(B, i)
C' = Mirror(C, i)
D' = Mirror(D, i)
E' = Mirror(E, i)
F' = Mirror(F, i)
poly1', a', b', c', d', e', f' = Polygon(A', B', C', D', E', F')
A'' = Mirror(A', j)
B'' = Mirror(B', j)
C'' = Mirror(C', j)
D'' = Mirror(D', j)
E'' = Mirror(E', j)
F'' = Mirror(F', j)
poly1'', a'', b'', c'', d'', e'', f'' = Polygon(A'', B'', C'', D'', E'', F'')
A''_1 = Mirror(A', j)
B''_1 = Mirror(B', j)
a''_1 = Segment(A''_1, B''_1)
B''_2 = Mirror(B', j)
C''_1 = Mirror(C', j)
b''_1 = Segment(B''_2, C''_1)
C''_2 = Mirror(C', j)
D''_1 = Mirror(D', j)
c''_1 = Segment(C''_2, D''_1)
D''_2 = Mirror(D', j)
E''_1 = Mirror(E', j)
d''_1 = Segment(D''_2, E''_1)
E''_2 = Mirror(E', j)
F''_1 = Mirror(F', j)
e''_1 = Segment(E''_2, F''_1)
F''_2 = Mirror(F', j)
A''_2 = Mirror(A', j)
f''_1 = Segment(F''_2, A''_2)
α_1 = Angle(H, K, J)
k = false
α = 0 rad (slider from 0 to Ang, step 1*°)
A'_1 = Rotate(A, α, K)
B'_1 = Rotate(B, α, K)
C'_1 = Rotate(C, α, K)
D'_1 = Rotate(D, α, K)
E'_1 = Rotate(E, α, K)
F'_1 = Rotate(F, α, K)
poly1'_1, a'_1, b'_1, c'_1, d'_1, e'_1, f'_1 = Polygon(A'_1, B'_1, C'_1, D'_1, E'_1, F'_1)
l = Segment(B, K)
m = Segment(K, B'_1)
β = Angle(B, K, B'_1)
Ang: 2 * α_1

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')