Obraz štvorca v osovej afinite

Zostrojte obraz štvorca ABCD v OA:  os  o = DS_A_B,  smer s = AA_1,  kde A_1=S_B_C

POSTUP:

1.

Je daný štvorec ABCD a stredy strán S_A_B a  S_B_C

OA je daná osou o = DS_A_B a smerom s = AS_B_C

2.

   = A_1

 = D_1

V OA: D = D_1,  A → A_1 odkiaľ dostávane, že AD → A_1D 

Obrazy bodov B a C budú ležať na rovnobežkách so smerom s

4.

a = AS_A_B  →  a_1 = A_1S_A_B, S_A_B  je samodružný 

5.

B → B_1, kde  B_1 ∈ s_b ∩ a_1 

Obrazom úsečky  AB  je úsečka  A_1B_1

6.

Úsečka DC ∥ A_1B_1 a zároveň BC ∩ B_1C_1 

7.

Obrazom štvorca ABCD je rovnobežník A_1B_1C_1D_1

w = true
A = (-1.5, -1.5)
B = (1.5, -1.5)
C = (1.5, 1.5)
D = (-1.5, 1.5)
j = Segment(B, A)
h = Segment(C, B)
g = Segment(D, C)
i = Segment(D, A)
S_{AB} = Intersect(j, yAxis)
S_{BC} = Intersect(h, xAxis)
o = Line(D, S_{AB})
a_3 = true
u = Vector(A, S_{BC})
p = Line(A, S_{BC})
S = Point(p)
b = true
s = Segment(D, S_{BC})
O = Point(p)
R = Point(p)
sa = Segment(O, R)
b_1 = Line(B, sa)
U = Point(b_1)
V = Point(b_1)
W = Point(b_1)
sb = Segment(W, U)
s_b = Segment(V, U)
sc = Line(C, sa)
Q = Point(sc)
C_3 = Point(sc)
C_2 = Point(sc)
s_c = Segment(Q, C_3)
sc_1 = Segment(C_3, C_2)
c = true
a = Line(A, B)
t = Ray(S_{BC}, S_{AB})
T = Point(t)
a_1 = Segment(S_{BC}, T)
d = true
B_1 = Intersect(sb, a_1)
v = true
l_1 = Segment(S_{BC}, B_1)
e = true
sd = Line(D, a_1)
C_1 = Intersect(sd, sc_1)
i_1 = Segment(D, C_1)
k = Line(C, B)
E = Intersect(o, k)
l = Line(E, B_1)
f = true
q1, n_1, h_2, a_2, r = Polygon(S_{BC}, D, C_1, B_1)
o_1 = true