Matica

\text{Nájdite obraz nevlastného bodu }C.

Bod A

Bod B

Bod C

\text{Pohybujte bodmi} A,B. \
\text{Bod } C \text{ je nevlastný, nájdite jeho obraz (= úbežník 2. druhu). Zmeňte súradnice bodu }C.

C

\text{3. Bod }C' \text{ ako obraz v }\mathcal{K}(S,o, A→A')

A2: 1
A3: 0
A4: -1
B2: 0
B3: 1
C2: 0
C3: 0
B4: -1
C4: 2
mKol: {{A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}}
text1: "\text{Matica kolineácie }:" + (LaTeX[mKol]) + ""
A = (2, 2)
A8: x(A)
A9: y(A)
A10: 1
ma: {{A8}, {A9}, {A10}}
maa: (mKol * ma)
A': (Element[maa, 1, 1] / Element[maa, 3, 1], Element[maa, 2, 1] / Element[maa, 3, 1])
text5 = SurdText(A')
text6: "A':" + (LaTeX[text5]) + ""
B = (-3, 2)
A13: x(B)
A14: y(B)
A15: 1
mb: {{A13}, {A14}, {A15}}
mbb: (mKol * mb)
B': (Element[mbb, 1, 1] / Element[mbb, 3, 1], Element[mbb, 2, 1] / Element[mbb, 3, 1])
text3 = SurdText(B')
text4: "B'" + (LaTeX[text3]) + ""
A18: 1
A19 = 2
A20: 0
C: (A18, A19)
c = Vector((0, 0), C)
mc: {{A18}, {A19}, {A20}}
m2: {{A18}, {A19}, {A20}}
text8: "\text{1. Matica }mc:
=" + (LaTeX[mc]) + ""
mcc: (mKol * mc)
text9: "\text{2. Matica }mKol×mc=" + (LaTeX[mcc]) + ""
C': (Element[mcc, 1, 1] / Element[mcc, 3, 1], Element[mcc, 2, 1] / Element[mcc, 3, 1])
text10 = SurdText(C')
text11: "C'" + (LaTeX[text10]) + ""
text12: "\text{3. Bod }  " + (LaTeX[text11]) + ""
S = Point(c)
P = (-1, 2)
Q = Point(xAxis)
f = Line(P, Q)
g = Line(A, c)
h = Line(A', Q)
i = Line(S, C)