Axes

Point C

Problem 5: Determine where the points L,M,N are sent under this transformation
 

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Problem 5

Triangle

O = (0, 0)
A = (0, 1)
B = (1, 0)
u = Vector(O, A)
v = Vector(O, B)
O' = (2, 0)
A' = (2.459971301050553, 0.7789650507563983)
B' = (4.5463145414337305, 0.47899724580860525)
u' = Vector(O', A')
v' = Vector(O', B')
C = (0.19901993539925522, 0.7968735764249233)
w = Vector(O, C)
C' = Translate(O', Vector[u * w * u' + v * w * v'])
z = Vector(O', C')
D = (0.2, 1)
E = (0.4, 1)
F = (0.6, 1)
G = (0.8, 1)
H = (1, 1)
I = Point(v)
J = Point(v)
K = (0.6, 0)
L_2 = Point(v)
M_2 = (1, 0.2)
N_1 = (1, 0.4)
P_1 = (1, 0.6)
Q_1 = (1, 0.8)
R_1 = Point(u)
S = Point(u)
T = Point(u)
U = Point(u)
a = Segment(A, H)
b = Segment(R_1, Q_1)
c = Segment(S, P_1)
d = Segment(T, N_1)
e = Segment(U, M_2)
f = Segment(D, I)
g = Segment(E, J)
h = Segment(F, K)
i = Segment(G, L_2)
j = Segment(H, B)
V = Point(u')
W = Point(u')
Z = Point(u')
A_1 = Point(u')
B_1 = Point(v')
C_1 = Point(v')
D_1 = Point(v')
E_1 = Point(v')
F_1 = Translate(B_1, u')
G_1 = Translate(C_1, u')
H_1 = Translate(D_1, u')
I_1 = Translate(E_1, u')
V' = Translate(V, v')
W' = Translate(W, v')
Z' = Translate(Z, v')
J_1 = Translate(A_1, v')
A'' = Translate(A', v')
k = Segment(F_1, B_1)
l_1 = Segment(G_1, C_1)
m_1 = Segment(H_1, D_1)
n_1 = Segment(I_1, E_1)
p_2 = Segment(A'', B')
q_2 = Segment(A_1, J_1)
r_2 = Segment(A', A'')
s = Segment(Z, Z')
t = Segment(W, W')
a_1 = Segment(V, V')
o = false
b_1 = false
P = (0.5392819231012331, 0.8953704676018105)
Q = (0.37515134913042525, 0.22425979975645338)
R = (0.7829863390511191, 0.23741576717324983)
poly1, r_1, p_1, q_1 = Polygon(P, Q, R)
p = Vector(O, P)
q = Vector(O, Q)
r = Vector(O, R)
Q' = Translate(O', Vector[q * u * u' + q * v * v'])
P' = Translate(O', Vector[p * u * u' + p * v * v'])
R' = Translate(O', Vector[r * u * u' + r * v * v'])
poly2, r', p', q' = Polygon(P', Q', R')
L = (0.28856256374188083, 0.492428640059999)
M = (0.5974846315239394, 0.2058922293635996)
N = (0.5974846315239394, 0.8013507078420545)
l = Vector(O, L)
m = Vector(O, M)
n = Vector(O, N)
L' = Translate(O', Vector[l * u * u' + l * v * v'])
M' = Translate(O', Vector[m * u * u' + m * v * v'])
N' = Translate(O', Vector[n * u * u' + n * v * v'])
c_1 = false
e_1 = false
text2: "$\frac{\Delta PQR}{\Delta P'Q'R'} = $" + (LaTeX[poly1 / poly2]) + ""
text3: "$ \Delta PQR= $" + (LaTeX[poly1]) + ""
text4: "$ \Delta P'Q'R'= $" + (LaTeX[poly2]) + ""
d_1 = false
K_1 = (1.309348526847813, 0.4431801944715556)
L_1 = (1.6317019888812654, 0.4342259316372931)
u_1 = Vector(K_1, L_1)