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¡Bien, la figura es simétrica!

Puntos sobre el eje de simetría

estado = 5 (slider from 1 to 5, step 1)
n: 6 - estado
n1 = false
n2 = false
n3 = false
n4 = false
inc1: {(1, -1), (1, 1)}
inc2: {(-2, -1), (-2, 1), (-1, -2), (-1, 2), (1, -2), (1, 2), (2, -1), (2, 1)}
xr = If(n1 ∨ n2 ∨ n3 ∨ n4, Random[4, 10 + If[n1 ∨ n2 ∨ n3 ∨ n4, 0, 0]], Random[4, 10 + If[n1 ∨ n2 ∨ n3 ∨ n4, 0, 0]])
yr = If(n1 ∨ n2 ∨ n3 ∨ n4, Random[-1, 2 + If[n1 ∨ n2 ∨ n3 ∨ n4, 0, 0]], Random[-1, 2 + If[n1 ∨ n2 ∨ n3 ∨ n4, 0, 0]])
r1: x = xr + Random[0, If[n1 ∨ n2 ∨ n3 ∨ n4, 1, 1]] / 2
r2: y = yr + Random[0, If[n1 ∨ n2 ∨ n3 ∨ n4, 1, 1]] / 2
r3 = Line((xr, yr), (xr, yr) + Element[inc1, Random[1, If[n1 ∨ n2 ∨ n3 ∨ n4, 2, 2]]])
r4 = Line((xr, yr), (xr, yr) + Element[inc2, Random[1, If[n1 ∨ n2 ∨ n3 ∨ n4, 8, 8]]])
A = (0, 4)
A' = If(n1, Mirror[A, r1], If[n2, Mirror[A, r2], If[n3, Mirror[A, r3], If[n4, Mirror[A, r4], (1000, 1000)]]])
AA = (5, 4)
B = (0, 2)
B' = If(n1, Mirror[B, r1], If[n2, Mirror[B, r2], If[n3, Mirror[B, r3], If[n4, Mirror[B, r4], (1000, 1000)]]])
BB = (5, 2)
C = (0, 0)
C' = If(n1, Mirror[C, r1], If[n2, Mirror[C, r2], If[n3, Mirror[C, r3], If[n4, Mirror[C, r4], (1000, 1000)]]])
CC = (5, 0)
D = (0, -2)
D' = If(n1, Mirror[D, r1], If[n2, Mirror[D, r2], If[n3, Mirror[D, r3], If[n4, Mirror[D, r4], (1000, 1000)]]])
DD = (5, -2)
E = (0, -4)
E' = If(n1, Mirror[E, r1], If[n2, Mirror[E, r2], If[n3, Mirror[E, r3], If[n4, Mirror[E, r4], (1000, 1000)]]])
EE = (5, -4)
completo = If(n ≟ 1 ∧ AA ≟ A' ∨ n ≟ 2 ∧ AA ≟ A' ∧ BB ≟ B' ∨ n ≟ 3 ∧ AA ≟ A' ∧ BB ≟ B' ∧ CC ≟ C' ∨ n ≟ 4 ∧ AA ≟ A' ∧ BB ≟ B' ∧ CC ≟ C' ∧ DD ≟ D' ∨ n ≟ 5 ∧ AA ≟ A' ∧ BB ≟ B' ∧ CC ≟ C' ∧ DD ≟ D' ∧ EE ≟ E', true, false)
puntoEje = If(n ≟ 1 ∧ A ≟ AA ∨ n ≟ 2 ∧ (A ≟ AA ∨ B ≟ BB) ∨ n ≟ 3 ∧ (A ≟ AA ∨ B ≟ BB ∨ C ≟ CC) ∨ n ≟ 4 ∧ (A ≟ AA ∨ B ≟ BB ∨ C ≟ CC ∨ D ≟ DD) ∨ n ≟ 5 ∧ (A ≟ AA ∨ B ≟ BB ∨ C ≟ CC ∨ D ≟ DD ∨ E ≟ EE), true, false)
a = Segment(A, AA)
polígono1, aa, a1, b, bb = Polygon(AA, A, B, BB)
polígono2, bb1, b1, c, cc = Polygon(BB, B, C, CC)
polígono3, cc1, c1, d, dd = Polygon(CC, C, D, DD)
polígono4, dd1, d1, e, ee = Polygon(DD, D, E, EE)