 \text{V kolineácii }\mathscr{K}(S, o, u) \text{ zostrojte obraz bodu } A;  \text{ priamky }a ( a∈A) \text{ a bodu }B ( B∈a).

$S$

o

$A$

1. \;\text{Obraz }A'\;\text{leží na } s_a=\overleftrightarrow{SA}

1

2. \; \text{Samodružný }1:(o∩a)=1

$U_1$

3. \; \text{Bod - úbežník: }U_1=a∩u

$U'_1_∞$

4.\;\text{Pre obraz úbežníka }U_1 \text{ platí: }U'_1_∞∈\overrightarrow{SU_1}

$U'_1_∞$

5. \; \text{Potom }a'=\overleftrightarrow{1U'_1_∞}:(a'∥\overleftrightarrow{SU_1})∧(1∈a')

$A'$

6. \; A': (a'∩\overleftrightarrow{SA})=A'

$B$

7. \; \text{Zvoľme si bod }B∈a

8.  \; \text{Pre obraz }B' \text{ platí: }B'=(a'∩\overleftrightarrow{SB})

$B'$

S = (-0.37120709770837135, 0.05360930412097645)
P = (-0.7851065914831531, -0.5435523268470609)
Q = (0.7577468451822877, 0.05193496449749518)
o = Line(P, Q)
U = (0.8653517735513434, 0.3187377070497313)
u = Line(U, o)
A = (-0.29697114488831916, -0.24969758882951962)
s_a = Line(S, A)
LUB = (0.13571840869140941, 0.37176338763548233)
a = Line(LUB, A)
D = Intersect(o, a)
C = Intersect(u, a)
f = Line(S, C)
E = Point(f)
F = Point(f)
v = Vector(E, F)
g = Line(D, f)
H = Point(g)
G = Point(g)
w = Vector(G, H)
a' = Line(D, H)
A' = Intersect(s_a, g)
B = Point(a)
h = Line(S, B)
I = Intersect(g, a')
B' = Intersect(h, g)