Rotation - Alternative Methods

In this file you can: 
(1).  Show construction lines in a basic rotation 
(2).  Begin with only Object and Image and show how to find the Centre of Rotation 
(3).  See an alternative method of constructing a rotation

Construction Lines

Centre of Rotation

Join two pairs of corresponding points

Find midpoints

Find perpendicular bisectors

Show Image

Show all

Alternative Construction

a = Line(B, C)
A = (-24, 14)
D = (-22, 14)
c = Circle(A, D)
E = Point(c)
b = Segment(A, D)
d = Segment(A, E)
α = Angle(D, A, E)
F = (2, 5)
G = (3, 1)
H = (6, -1)
I = (8, -1)
J = (10, 6)
K = (9, 5)
L = (6, 8)
M = (4, 4)
poly1, f, g, h, i, j, k, l, m = Polygon(F, G, H, I, J, K, L, M)
N = (-8, 2)
F' = Rotate(F, α, N)
G' = Rotate(G, α, N)
H' = Rotate(H, α, N)
I' = Rotate(I, α, N)
J' = Rotate(J, α, N)
K' = Rotate(K, α, N)
L' = Rotate(L, α, N)
M' = Rotate(M, α, N)
poly1', f', g', h', i', j', k', l', m' = Polygon(F', G', H', I', J', K', L', M')
e = Segment(N, G)
n = Segment(N, G')
β = Angle(G, N, G')
p = CircleArc(N, G, G')
q = CircleArc(N, I, I')
r = CircleArc(N, J, J')
s = CircleArc(A, D, E)
o = false
t = false
a_1 = Segment(F', F)
O = Midpoint(F', F)
b_1 = Segment(I', I)
P = Midpoint(I', I)
c_5 = OrthogonalLine(O, a_1)
d_1 = OrthogonalLine(P, b_1)
Q = Intersect(c_5, d_1)
γ = Angle(Q, O, F)
δ = Angle(I', P, Q)
u = false
v = false
w = false
e_1 = OrthogonalLine(H, xAxis)
f_1 = OrthogonalLine(N, e_1)
R = Intersect(e_1, f_1)
g_1 = Circle(N, R)
S = (-24, 10)
T = (-22, 10)
h_1 = Circle(S, Segment[A, D])
z = Vector(A, E)
S' = Translate(S, z)
u_1 = Vector(S, S')
U = (-24, 10)
k_1 = CircleArc(U, T, S')
V = Point(k_1)
i_1 = Segment(U, T)
j_1 = Segment(U, V)
p_1 = CircleArc(U, T, V)
ε = Angle(T, U, V)
R' = Rotate(R, ε, N)
q_1 = Circle(R', Segment[R, H])
l_1 = Segment(N, R')
o_1 = false
v_1 = Vector(R, H)
R'' = Translate(R', v_1)
w_1 = Vector(R', R'')
R''' = Rotate(R'', ε, R')
m_1 = Segment(R', R''')
r_1 = Circle(N, 2)
n_1 = Line(N, xAxis)
W = Intersect(r_1, n_1, 2)
s_1 = Circle(W, N)
Z = Intersect(s_1, n_1, 2)
t_1 = Segment(N, Z)
a_2 = Segment(U, V)
ζ = Angle(Z, N, R')
A_1 = (-24, 4)
B_1 = (-22, 4)
c_2 = Circle(A_1, B_1)
C_1 = Rotate(B_1, α, A_1)
d_2 = CircleArc(A_1, B_1, C_1)
D_1 = Point(d_2)
b_2 = Segment(A_1, B_1)
e_2 = Segment(A_1, D_1)
f_2 = CircleArc(A_1, B_1, D_1)
g_2 = OrthogonalLine(I, xAxis)
h_2 = OrthogonalLine(N, yAxis)
E_1 = Intersect(g_2, h_2)
z_1 = Vector(E_1, I)
k_2 = Circle(N, Segment[N, E_1])
η = Angle(B_1, A_1, D_1)
F_1 = Rotate(E_1, η, N)
p_2 = Circle(F_1, Segment[E_1, I])
G_1 = Translate(F_1, z_1)
u_2 = Vector(F_1, G_1)
H_1 = Rotate(G_1, η, F_1)
i_2 = Segment(F_1, H_1)
j_2 = Segment(N, F_1)
I_1 = Point(k_2)
l_2 = OrthogonalLine(J, xAxis)
J_1 = Intersect(l_2, h_2)
q_2 = Circle(N, Segment[J_1, N])
K_1 = Rotate(J_1, η, N)
r_2 = Circle(K_1, Segment[J_1, J])
v_2 = Vector(J_1, J)
L_1 = Translate(K_1, v_2)
w_2 = Vector(K_1, L_1)
M_1 = Rotate(L_1, η, K_1)
m_2 = Segment(K_1, M_1)
n_2 = Segment(N, K_1)
s_2 = OrthogonalLine(K, xAxis)
N_1 = Intersect(s_2, h_2)
z_2 = Vector(N_1, K)
t_2 = Circle(N, Segment[N_1, N])
O_1 = Rotate(N_1, η, N)
c_3 = Circle(O_1, Segment[N_1, K])
P_1 = Translate(O_1, z_2)
u_3 = Vector(O_1, P_1)
Q_1 = Rotate(P_1, η, O_1)
a_3 = Segment(O_1, Q_1)
b_3 = Segment(N, O_1)
d_3 = OrthogonalLine(L, xAxis)
R_1 = Intersect(h_2, d_3)
v_3 = Vector(R_1, L)
e_3 = Circle(N, Segment[N, R_1])
S_1 = Rotate(R_1, η, N)
T_1 = Translate(S_1, v_3)
w_3 = Vector(S_1, T_1)
U_1 = Rotate(T_1, η, S_1)
f_3 = Segment(S_1, U_1)
g_3 = Segment(N, S_1)
h_3 = OrthogonalLine(M, xAxis)
V_1 = Intersect(h_3, h_2)
k_3 = Circle(N, Segment[N, V_1])
z_3 = Vector(V_1, M)
W_1 = Rotate(V_1, η, N)
Z_1 = Translate(W_1, z_3)
i_3 = Vector(W_1, Z_1)
A_2 = Rotate(Z_1, η, W_1)
j_3 = Segment(W_1, A_2)
l_3 = Segment(N, W_1)
m_3 = OrthogonalLine(F, xAxis)
B_2 = Intersect(m_3, h_2)
n_3 = Vector(B_2, F)
p_3 = Circle(N, Segment[N, B_2])
C_2 = Rotate(B_2, η, N)
D_2 = Translate(C_2, n_3)
q_3 = Vector(C_2, D_2)
E_2 = Rotate(D_2, η, C_2)
r_3 = Segment(C_2, N)
s_3 = Segment(C_2, E_2)
t_3 = OrthogonalLine(G, xAxis)
F_2 = Intersect(t_3, h_2)
c_4 = Circle(N, Segment[N, F_2])
u_4 = Vector(F_2, G)
G_2 = Rotate(F_2, η, N)
H_2 = Translate(G_2, u_4)
v_4 = Vector(G_2, H_2)
I_2 = Rotate(H_2, η, G_2)
a_4 = Segment(G_2, I_2)
b_4 = Segment(N, G_2)
F'_1 = Rotate(F, η, N)
G'_1 = Rotate(G, η, N)
H'_1 = Rotate(H, η, N)
I'_1 = Rotate(I, η, N)
J'_1 = Rotate(J, η, N)
K'_1 = Rotate(K, η, N)
L'_1 = Rotate(L, η, N)
M'_1 = Rotate(M, η, N)
poly1'_1, f'_1, g'_1, h'_1, i'_1, j'_1, k'_1, l'_1, m'_1 = Polygon(F'_1, G'_1, H'_1, I'_1, J'_1, K'_1, L'_1, M'_1)
c_1 = false
o_2 = false