\text{Podmienka (AP1): pre body } X=[x_1,x_2), \; Y=[y_1,y_2), \; Z=[z_1,z_2) \text{ dostávame:}\ \
\blue {f(X,Y)+f(Y,Z)=\left (x_1-y_1,x_2-y_2  \right)   +\left (y_1-z_1,y_2-z_2  \right)} = \red{\left ( x_1-z_1,x_2-z_2 \right ) =f(X,Z)}.

\text{Podmienka (AP2):} \text{ Nech } 
P=[p_1,p_2] \text{ je pevne zvolený bod, potom pre obrazy}\\\
\darkgreen {f(P,X)=\left [p_1-x_1,p_2-x_2  \right ]} \
\darkgreen {f(P,Y)=\left [ p_1-y_1,p_2-y_2 \right ]} \\\
\text{platí, že sú rôzne. Teda zobrazenie }f_P\text{ je bijektívne.}

X = (1, 1)
Y = (6, 3)
u = Vector(X, Y)
A = Midpoint(X, Y)
u1: x(u)
u2: y(u)
Z = (2, 8)
B = Midpoint(Z, Y)
v = Vector(Y, Z)
text2: "\vec u= (" + (LaTeX[u1]) + "," + (LaTeX[u2]) + ")"
v1: x(v)
v2: y(v)
text3: "\vec v=(" + (LaTeX[v1]) + "," + (LaTeX[v2]) + ")"
w = Vector(X, Z)
w1: x(w)
w2: y(w)
text6: "\vec w=\vec u + \vec v =( " + (LaTeX[w1]) + ", " + (LaTeX[w2]) + ")"
P = (-2, 2)
a = Vector(P, X)
X_{1} = (3, -1)
b = Vector(P, Y)
P_{1} = (0, 0)