Translation using tracing paper

Tracing Paper

A_1 = (-8, 8)
B_1 = (-7, 13)
C_1 = (-3, 13)
D_1 = (-3, 11)
E = (-6, 11)
F = (-6, 7)
poly1, a, b, c, d, e, f = Polygon(A_1, B_1, C_1, D_1, E, F)
Drag = (-8, 8)
g = Circle(Drag, 2)
Angle = Point(g)
h = Line(Drag, Angle)
A = Point(h)
i = OrthogonalLine(Drag, h)
C = Point(h)
G' = Rotate(Drag, 45*°, C)
α = Angle(Drag, C, G')
G'_1 = Rotate(Drag, 45*°, A)
β = Angle(Drag, A, G'_1)
G'_2 = Rotate(Drag, 315*°, A)
γ = Angle(G'_2, A, Drag)
j = Line(A, G'_2)
k = Line(C, G')
B = Intersect(j, k)
D = Mirror(B, h)
G = (-5.171533888251223, 8.397012648230445)
l = Line(A, C)
m: y - y(Drag) = x - x(Drag)
I = Intersect(g, m, 1)
δ = Angle(I, Drag, Angle)
J = Rotate(A_1, δ, Drag)
K = Rotate(B_1, δ, Drag)
L = Rotate(C_1, δ, Drag)
M = Rotate(D_1, δ, Drag)
E' = Rotate(E, δ, Drag)
F' = Rotate(F, δ, Drag)
poly1', j_1, k_1, l_1, m_1, e', f' = Polygon(J, K, L, M, E', F')
n = Line(Drag, xAxis)
p = Ray(Angle, Drag)
H = Intersect(g, p, 2)
H' = Rotate(H, 315*°, Drag)
ε = Angle(H', Drag, H)
q = Ray(Drag, H')
r = OrthogonalLine(A_1, n)
s = OrthogonalLine(J, q)
N = Intersect(s, q)
O = Intersect(r, n)
t = Segment(Drag, O)
a_1 = Segment(O, A_1)
b_1 = Line(H', Drag)
c_1 = OrthogonalLine(J, b_1)
P = Intersect(b_1, c_1)
d_1 = Segment(Drag, P)
e_1 = Segment(P, J)
ζ = Angle(P, Drag, O)
u = Vector(A_1, Drag)
Q = Translate(A_1, u)
R = Translate(B_1, u)
S = Translate(C_1, u)
T = Translate(D_1, u)
E'_1 = Translate(E, u)
F'_1 = Translate(F, u)
poly1'_1, q_1, r_1, s_1, t_1, e'_1, f'_1 = Polygon(Q, R, S, T, E'_1, F'_1)
o = false
f_1 = Line(A_1, xAxis)
g_1 = Line(Drag, yAxis)
U = Intersect(f_1, g_1)
h_1 = Segment(A_1, U)
i_1 = Segment(U, Drag)
V = Midpoint(h_1)
W = Midpoint(i_1)
ipn = If(y(Q) - y(A_1) ≥ 0, y(Q) - y(A_1), y(A_1) - y(Q))
text1 = If(x(Q) ≥ x(A_1), d_1 + "", If[x(Q) < x(A_1), -1 * d_1 + "", 0])
text2 = If(y(Q) ≥ y(A_1), i_1 + "", If[y(Q) < y(A_1), -1 * i_1 + "", 0])
text3: "\left\begin{bmatrix}x\\y\end{bmatrix}\right=\left\begin{bmatrix}" + (LaTeX[If[x(Q) > x(A_1), d_1 + "", If[x(Q) < x(A_1), -1 * d_1 + "", "0"]]]) + " \\" + (LaTeX[If[y(Q) > y(A_1), i_1 + "", If[y(Q) < y(A_1), -1 * i_1 + "", "0"]]]) + "\end{bmatrix}\right"