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 5

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 e

Vector f

18
 9

A = (-12.42, -0.86)
B = (-4.42, 3.14)
u = Vector(A, B)
C = (-7, 1)
D = (-5, 2)
v = Vector(C, D)
E = (12.04, 1.44)
E' = Translate(E, u)
w = Vector(E, E')
N = (13, 8)
O = (17.86, 8.06)
P = (17.88, 4.58)
Q = (13.02, 4.56)
N_1 = (12.64, 4.26)
O_1 = (17.5, 4.32)
P_1 = (17.5, 0.74)
Q_1 = (12.62, 0.72)
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)
A_3 = (-5.5, 1.7)
B_3 = (-2.5, 3.7)
A_4 = (-6.76, 3)
B_4 = (-3.76, 5)
A_5 = (-6.72, 2.54)
B_5 = (-3.72, 4.54)
A_6 = (-6.54, 2.26)
B_6 = (-3.54, 4.26)
A_7 = (-6.56, 1.76)
B_7 = (-3.56, 3.76)
A_8 = (-6.32, 1.64)
B_8 = (-3.32, 3.64)
C_2 = (-6.78, 0.78)
D_2 = (-2.78, 1.78)
C_3 = (-6.72, 1.26)
D_3 = (-2.72, 2.26)
C_4 = (-6.72, 1.64)
D_4 = (-2.72, 2.64)
C_5 = (-7.1, 0.78)
D_5 = (-3.1, 1.78)
C_6 = (-7.26, 1.06)
D_6 = (-3.26, 2.06)
C_7 = (-6.44, 0.98)
D_7 = (-4.44, 1.98)
C_8 = (-6.08, 0.82)
D_8 = (-4.08, 1.82)
C_9 = (-7.6, 1.5)
D_9 = (-5.6, 2.5)
C_{10} = (-7.4, 1.88)
D_{10} = (-5.4, 2.88)
C_{11} = (-6.84, 1.72)
D_{11} = (-4.84, 2.72)
C_{12} = (-8.18, 1.36)
D_{12} = (-6.18, 2.36)
A_9 = (-8.18, 2.26)
B_9 = (-7.18, 4.26)
A_{10} = (-8.02, 2.18)
B_{10} = (-7.02, 4.18)
A_{11} = (-5.54, 1.8)
B_{11} = (-4.54, 3.8)
A_{12} = (-7.28, 1.82)
B_{12} = (-6.28, 3.82)
A_{13} = (-5.02, 1.72)
B_{13} = (-4.02, 3.72)
A_{14} = (-6.76, 1.72)
B_{14} = (-5.76, 3.72)
A_{15} = (-5.9, 1.6)
B_{15} = (-4.9, 3.6)
G_2 = (11.74, 1.68)
H_2 = (11.76, 1.18)
I_2 = (11.98, 0.96)
K_2 = Translate(G_2, u)
u_1 = Vector(G_2, K_2)
L_2 = Translate(H_2, u)
v_1 = Vector(H_2, L_2)
M_2 = Translate(I_2, u)
w_1 = Vector(I_2, M_2)
F = (0.56, 6.6)
G = (1.92, 6.62)
H = (1.72, 6.78)
I = (0.88, 6.56)
I' = Translate(I, v)
a = Vector(I, I')
H' = Translate(H, v)
b = Vector(H, H')
F' = Translate(F, v)
c = Vector(F, F')
G' = Translate(G, v)
d = Vector(G, G')
J = (0.6, 6.7)
K = (2.26, 6.78)
L = (2.38, 6.54)
M = (1.2, 6.54)
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')
K_1 = (11.76, 0.56)
L_1 = (11.98, 1.96)
M_1 = (12.02, 0.12)
R_1 = (12.12, 0.4)
S_1 = Translate(K_1, u)
m = Vector(K_1, S_1)
T_1 = Translate(L_1, u)
r = Vector(L_1, T_1)
U_1 = Translate(M_1, u)
s = Vector(M_1, U_1)
V_1 = Translate(R_1, u)
t = Vector(R_1, V_1)