Verschieben

v_x

v_y

Spiegeln

Ausgangsposition

Strecken

Drehen

zSpiegelnGewaehlt

A = (6, -4)
B = (14, -4)
D = (6, 4)
C: B + Vector[A, D]
M: A + (1 / 2 * (C - A))
L: -15
R: 15
U: -15
O: 15
Sx: {{1, 0}, {0, -1}}
B' = (-14, -4)
v1 = 10 (slider from -100 to 100, step 0.1)
v2 = 0 (slider from -100 to 100, step 0.5)
D' = (-6, 4)
A' = (-6, -4)
C': B' + D' - A'
V: (v1, v2)
v' = Vector(V)
Sy: {{-1, 0}, {0, 1}}
MAB: A + (1 / 2 * (B - A))
MCD: C + (1 / 2 * (D - C))
gS = Line(MAB, MCD)
orientierung = -1 (slider from -5 to 5, step 0.1)
S2: D + (1 / 2 * (C - D)) + ((orientierung * 8) * UnitOrthogonalVector[C - D])
S1: A + (1 / 2 * (B - A)) - ((orientierung * 8) * UnitOrthogonalVector[B - A])
sStrecken = Segment(S1, S2)
S = Point(sStrecken)
k: Segment[V, S] / Segment[V, MCD]
Sk: {{k, 0}, {0, k}}
M': A' + (1 / 2 * (C' - A'))
e = Circle(M, A)
E = Point(e)
E' = (15.503022969475515, -1.310243564160837)
α = Angle(E', V, E)
Sw: {{cos(α), (-sin(α))}, {sin(α), cos(α)}}
Text1: "A = " + (LaTeX[A]) + " \\
B = " + (LaTeX[B]) + " \\
C = " + (LaTeX[C]) + " \\
D = " + (LaTeX[D]) + ""
Text2: "A' = " + (LaTeX[A']) + " \\
B' = " + (LaTeX[B']) + " \\
C' = " + (LaTeX[C']) + " \\
D' = " + (LaTeX[D']) + ""
zustandAnzeigen: zustand ≟ "zVerschiebenGewaehlt" ∨ zustand ≟ "zSpiegelnGewaehlt" ∨ zustand ≟ "zStreckenGewaehlt" ∨ zustand ≟ "zDrehenGewaehlt" ∨ zustand ≟ "zSpiegelnXAchseAngezeigt" ∨ zustand ≟ "zSpiegelnYAchseAngezeigt" ∨ zustand ≟ "zStreckenAngezeigt"
P = (0, -10)
Q = (0, 10)
g = Line(P, Q)
aOg = Distance((0, 0), g)
nOg: (aOg * UnitOrthogonalVector[g])
n = Line((0, 0), Vector[OrthogonalVector[Vector[P, Q]]])
NOg = Intersect(g, n)
v = Vector(M, V)
f = Segment(E', V)
h = Segment(E, V)
m = Slope(g)
β = If(x(P) ≟ x(Q), 90°, atand(m))
sp = 1 (slider from -5 to 5, step 0.1)
Ssp: {{cos((2 * β)), sin((2 * β))}, {sin((2 * β)), (-cos((2 * β)))}}
zentrumAnzeigen: zustand ≟ "zStreckenGewaehlt" ∨ zustand ≟ "zDrehenGewaehlt" ∨ zustand ≟ "zVerschiebenGewaehlt" ∨ zustand ≟ "zStreckenAngezeigt"
Ursprung: (0, 0)
F = (-8.314285714285713, -18.3)
G = (-2.6990476190476116, -18.3)
H = (-8.314285714285713, -18.3)
I: (-2.6990476190476116, -18.3)
RahmenBild1, a, b, c, d = Polygon(A, B, C, D)
RahmenBild2, a', b', c', d' = Polygon(A', B', C', D')
Text3: "\vec{a} = \begin{pmatrix} " + (LaTeX[x(A)]) + " \\ " + (LaTeX[y(A)]) + " \end{pmatrix}"
Text4: "\vec{a'} = \begin{pmatrix} " + (LaTeX[x(A')]) + "  \\  " + (LaTeX[y(A')]) + " \end{pmatrix}"
Text5: "A(" + (LaTeX[x(A)]) + "|" + (LaTeX[y(A)]) + ")"
Text6: "A'(" + (LaTeX[x(A')]) + "|" + (LaTeX[y(A')]) + ")"
i = Segment(A, A')