2

1

M_s

m⁻¹

\text{Transformačné rovnice }

$sam$

\text{Pohybujte trojuholníkmi alebo vrcholmi trojuholníkov.}

a

b

c

d

p

q

X'

C = (-3, 0)
A = (-1, -2)
B = (1.5, -1.5)
k = Line(C, B)
g = Line(A, B)
A' = (4, 2)
i = Line(A, A')
m = Line(C, i)
j = Line(B, i)
D = Point(yAxis)
E = Point(xAxis)
f = Line(D, E)
H = Intersect(k, f)
F = Intersect(g, f)
h = Line(F, A')
G = Intersect(j, h)
l = Line(H, G)
I = Intersect(m, l)
t1, c, a, b = Polygon(A, B, C)
B': G
C': I
t2, c', a', b' = Polygon(A', B', C')
A1: x(A)
A2: y(A)
B1: x(B)
B2: y(B)
C1: x(C)
C2: y(C)
A3: 1
B3: 1
C3: 1
A6: x(A')
A7: y(A')
B6: x(B')
B7: y(B')
C6: x(C')
C7: y(C')
A8: 1
B8: 1
C8: 1
maticavstup: {{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}}
text3: "\text{Matica vzorov } \\\\" + (LaTeX[maticavstup]) + ""
maticavystup: {{A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}}
text4: "\text{Matica obrazov } \\\\ " + (LaTeX[maticavystup]) + ""
matinverz: maticavstup^(-1)
rovnice: (maticavystup * matinverz)
a11 = SurdText(Element[rovnice, 1, 1])
a21 = SurdText(Element[rovnice, 2, 1])
b12 = SurdText(Element[rovnice, 1, 2])
b22 = SurdText(Element[rovnice, 2, 2])
p = SurdText(Element[rovnice, 1, 3])
q = SurdText(Element[rovnice, 2, 3])
b2 = If(Element[rovnice, 2, 2] < 0, " ", "+")
p1 = If(Element[rovnice, 1, 3] < 0, " ", "+")
b1 = If(Element[rovnice, 1, 2] < 0, " ", "+")
p2 = If(Element[rovnice, 2, 3] < 0, " ", "+")
text1: "x'= " + (LaTeX[a11]) + "x" + (LaTeX[b1]) + "" + (LaTeX[b12]) + "y" + (LaTeX[p1]) + "" + (LaTeX[p]) + "   \\\\
y'=" + (LaTeX[a21]) + "x" + (LaTeX[b2]) + "" + (LaTeX[b22]) + "y" + (LaTeX[p2]) + "" + (LaTeX[q]) + ""
R = (-2, 1)
A11: x(R)
A12: y(R)
A13: 1
rrbod: {{A11}, {A12}, {A13}}
rr'bod: (rovnice * rrbod)
R': (Element[rr'bod, 1, 1], Element[rr'bod, 2, 1])
u = Vector(R, R')
sam1: ((Element[rovnice, 1, 1] - 1) * x) + (Element[rovnice, 1, 2] * y) + Element[rovnice, 1, 3] = 0
sam2: (Element[rovnice, 2, 1] * x) + ((Element[rovnice, 2, 2] - 1) * y) + Element[rovnice, 2, 3] = 0
SAM = If(sam1 ≠ sam2, Intersect[sam1, sam2])
text5: "\text{ Množina samodružných bodov}\\\\
 \ \;  \; \text{SAM: }   \left\{   " + (LaTeX[sam1]) + "  \right\} "
text6: "\text{ Množina samodružných bodov}\\\\
 \ \;  \; \text{SAM: }    \left\{  " + (LaTeX[SAM]) + "  \right\}  "
text7 = If(sam1 ≟ sam2, text5, text6)
A16: x(A)
C16: y(A)
E16: 1
G16: x(A')
F17: 1
G17: y(A')
B17: x(A)
D17: y(A)
A18: x(B)
C18: y(B)
E18: 1
G18: x(B')
B19: x(B)
D19: y(B)
F19: 1
A20: x(C)
C20: y(C)
E20: 1
G20: x(C')
G19: y(B')
B21: x(C)
D21: y(C)
F21: 1
G21: y(C')
B16: 0
D16: 0
F16: 0
A17: 0
C17: 0
E17: 0
A19: 0
C19: 0
B18: 0
D18: 0
F18: 0
E19: 0
B20: 0
D20: 0
F20: 0
A21: 0
C21: 0
E21: 0