Use the visual representation of vectors a and b to show 
how to reach the combination of 

Is there more than one way that would work? 
Why or Why not?

Reaching Your Goal 1

Be sure to record what you have found. 
Sketch it in your notebook and use 
vector component notation or 
matrix notation to show what is happening.

Vector a

Vector b

18
 7

A = (-6, 2)
B = (-3, 4)
u = Vector(A, B)
C = (-7, 1)
D = (-3, 2)
v = Vector(C, D)
E = (1.44, 3.82)
F = (1.36, 5.06)
G = (1, 5)
H = (1.26, 4.6)
I = (1.24, 4.14)
J = (0.74, 8.1)
K = (0.64, 8.26)
L = (0.7, 8.62)
M = (1, 9)
E' = Translate(E, u)
w = Vector(E, E')
F' = Translate(F, u)
a = Vector(F, F')
G' = Translate(G, u)
b = Vector(G, G')
H' = Translate(H, u)
c = Vector(H, H')
I' = Translate(I, u)
d = Vector(I, I')
J' = Translate(J, v)
e = Vector(J, J')
K' = Translate(K, v)
f = Vector(K, K')
L' = Translate(L, v)
g = Vector(L, L')
M' = Translate(M, v)
h = Vector(M, M')
N = (0.44, 10.28)
O = (5.3, 10.34)
P = (5.3, 7.7)
Q = (0.44, 7.68)
poly1, n, o, p, q = Polygon(N, O, P, Q)
N_1 = (0.4, 7.22)
O_1 = (5.26, 7.28)
P_1 = (5.3, 3.28)
Q_1 = (0.42, 3.26)
poly1_1, n_1, o_1, p_1, q_1 = Polygon(N_1, O_1, P_1, Q_1)
R = (13.9, 9.7)
S = (13.68, 9.44)
T = (13.84, 9.18)
U = (15.04, 9.68)
V = (15.22, 9.44)
W = (15.08, 9.16)
Z = (14.18, 8.72)
A_1 = (13.84, 8.72)
i = Segment(Z, A_1)
B_1 = (13.84, 9.88)
j = Segment(A_1, B_1)
C_1 = (14.22, 9.88)
k = Segment(B_1, C_1)
D_1 = (14.4, 10.16)
E_1 = (14.4, 7.94)
l = Line(D_1, E_1)
F_1 = Mirror(A_1, l)
G_1 = Mirror(B_1, l)
j' = Segment(F_1, G_1)
Z' = Mirror(Z, l)
H_1 = Mirror(A_1, l)
i' = Segment(Z', H_1)
I_1 = Mirror(B_1, l)
J_1 = Mirror(C_1, l)
k' = Segment(I_1, J_1)
A_2 = (-5.64, 1.94)
B_2 = (-2.64, 3.94)
u_1 = Vector(A_2, B_2)
A_3 = (-5.5, 1.7)
B_3 = (-2.5, 3.7)
u_2 = Vector(A_3, B_3)
A_4 = (-6.76, 3)
B_4 = (-3.76, 5)
u_3 = Vector(A_4, B_4)
E_4 = (0.74, 5.1)
E'_3 = Translate(E_4, u_3)
w_3 = Vector(E_4, E'_3)
A_5 = (-6.72, 2.54)
B_5 = (-3.72, 4.54)
u_4 = Vector(A_5, B_5)
E_5 = (0.72, 4.5)
E'_4 = Translate(E_5, u_4)
w_4 = Vector(E_5, E'_4)
A_6 = (-6.54, 2.26)
B_6 = (-3.54, 4.26)
u_5 = Vector(A_6, B_6)
E_6 = (0.68, 4.12)
E'_5 = Translate(E_6, u_5)
w_5 = Vector(E_6, E'_5)
A_7 = (-6.56, 1.76)
B_7 = (-3.56, 3.76)
u_6 = Vector(A_7, B_7)
E_7 = (1.94, 3.58)
E'_6 = Translate(E_7, u_6)
w_6 = Vector(E_7, E'_6)
A_8 = (-6.32, 1.64)
B_8 = (-3.32, 3.64)
u_7 = Vector(A_8, B_8)
E_8 = (1.4, 3.46)
E'_7 = Translate(E_8, u_7)
w_7 = Vector(E_8, E'_7)
C_2 = (-6.78, 0.78)
D_2 = (-2.78, 1.78)
v_1 = Vector(C_2, D_2)
J_2 = (0.78, 8.44)
J'_1 = Translate(J_2, v_1)
e_1 = Vector(J_2, J'_1)
C_3 = (-6.72, 1.26)
D_3 = (-2.72, 2.26)
v_2 = Vector(C_3, D_3)
J_3 = (1.2, 7.82)
J'_2 = Translate(J_3, v_2)
e_2 = Vector(J_3, J'_2)
C_4 = (-6.72, 1.64)
D_4 = (-2.72, 2.64)
v_3 = Vector(C_4, D_4)
J_4 = (1.06, 8.6)
J'_3 = Translate(J_4, v_3)
e_3 = Vector(J_4, J'_3)
C_5 = (-7.1, 0.78)
D_5 = (-3.1, 1.78)
v_4 = Vector(C_5, D_5)
J_5 = (0.84, 9.12)
J'_4 = Translate(J_5, v_4)
e_4 = Vector(J_5, J'_4)
C_6 = (-7.26, 1.06)
D_6 = (-3.26, 2.06)
v_5 = Vector(C_6, D_6)
J_6 = (1, 8)
J'_5 = Translate(J_6, v_5)
e_5 = Vector(J_6, J'_5)