O

\overrightarrow{i}

\overrightarrow{j}

\mathcal{R}

(0,0)

(1,0)

(0,1)

t

M

\overrightarrow{u}

\left(\begin{array}{} \textcolor{white}{i} \ \textcolor{white}{i} \ \textcolor{white}{i} \end{array} \right.

\left.\begin{array}{} \textcolor{white}{i} \ \textcolor{white}{i} \ \textcolor{white}{i} \end{array} \right)

x+

y=

d

||\overrightarrow{i}||=

,\,||\overrightarrow{j}||=

\text{angle de }\overrightarrow{i}\text{ vers }\overrightarrow{j}=

\left\{\begin{array}{} x= \ \textcolor{white}{i}\ \textcolor{white}{i}  \ y= \end{array}\right. 

+

+

t

t

,\,t\in\mathbb{R}

,\,t=

x

\left\{\begin{array}{} x'= \ \vspace{5mm} \ y'= \end{array} \right.

(x,y)

(x',y')

x

y=

x+

x+

x

y=

\left\{\begin{array}{} x= \ \textcolor{white}{i}\ \textcolor{white}{i}  \ y= \end{array}\right. 

+

+

t

t

,\,t\in\mathbb{R}

,\,t=

\text{hauteurs}

\text{bissectrices}

\text{médiatrices}

\text{médianes}

q_1 = 0 (slider from -10 to 10, step 0.1)
p_1 = 0 (slider from -10 to 10, step 0.1)
A = (-26.88699977914943, 1.1854756095049521)
B = (-22.077283185285953, 4.990897648065568)
C: (x(A), y(B))
D: (x(B), y(A))
q1, a, d, b, c = Polygon(A, D, B, C)
E = PointIn(q1)
F = PointIn(q1)
G = PointIn(q1)
e = 1 (slider from 0.1 to 5, step 0.1)
g = Circle(E, e)
H = Point(g)
f = 1 (slider from 0.1 to 5, step 0.1)
h: f / e
α = 1.5707963267948966 rad (slider from -3.141592653589793 to 3.141592653589793, step 0.017453292519943295)
H' = Rotate(H, α, E)
L: E + (h * Vector[E, H'])
n = 1 (slider from 0 to 1, step 1)
J = If(n ≟ 0, G, L)
v = Vector(E, J)
I = If(n ≟ 0, F, H)
u = Vector(E, I)
V = (-27.886139238061865, 4.516051636362547)
i = 0 (slider from 0 to 1, step 1)
K: E + (0.5 * u)
M: E + (0.5 * v)
j = true
k = 0 (slider from 0 to 2, step 1)
N: (2, 1)
ChampTexte1 = Textfield(N)
m1: {{x(u), x(v)}, {y(u), y(v)}}
O: E + (x(N) * u) + (y(N) * v)
l = Line(E, u)
m = Line(E, v)
w: (2, 1)
Q = (9.850382614414434, 4.532544654623457)
o = 0 (slider from -50 to 50, step 0.1)
p = 0 (slider from -10 to 10, step 0.1)
q = 0 (slider from -10 to 30, step 0.1)
ChampTexte5 = Textfield(o)
ChampTexte6 = Textfield(p)
ChampTexte7 = Textfield(q)
r: o^(2) + p^(2)
s = If(r ≠ 0, ((o * q)) / r)
a_1 = If(r ≠ 0, ((p * q)) / r)
f_1 = If(r ≠ 0, Line[E + (s * u) + (a_1 * v), Vector[((-p) * u) + (o * v)]])
b_1 = 0 (slider from -10 to 10, step 0.1)
c_1 = 0 (slider from -10 to 10, step 0.1)
d_1 = 0 (slider from -10 to 10, step 0.1)
e_1 = 0 (slider from -10 to 10, step 0.1)
ChampTexte8 = Textfield(b_1)
ChampTexte9 = Textfield(c_1)
ChampTexte10 = Textfield(d_1)
ChampTexte11 = Textfield(e_1)
g_1 = -2.22 (slider from -5 to 5, step 0.01)
h_1 = If(c_1^(2) + e_1^(2) ≠ 0, Line[E + (b_1 * u) + (d_1 * v), Vector[(c_1 * u) + (e_1 * v)]])
R: E + ((b_1 + (g_1 * c_1)) * u) + ((d_1 + (e_1 * g_1)) * v)
S: (3, 4)
T: (10, 3)
U: (0, 0)
W: (0, 0)
Z: (0, 0)
ChampTexte12 = Textfield(S)
ChampTexte13 = Textfield(T)
ChampTexte14 = Textfield(U)
ChampTexte15 = Textfield(W)
ChampTexte16 = Textfield(Z)
texte14: "" + (LaTeX[U]) + ""
texte15: "" + (LaTeX[W]) + ""
texte16: "" + (LaTeX[Z]) + ""
A_1: E + (x(S) * u) + (y(S) * v)
B_1: E + (x(T) * u) + (y(T) * v)
C_1: E + (x(U) * u) + (y(U) * v)
D_1: E + (x(W) * u) + (y(W) * v)
E_1: E + (x(Z) * u) + (y(Z) * v)
n_1 = 1 (slider from 0 to 1, step 1)
i_1 = 1 (slider from 0 to 1, step 1)
j_1 = 1 (slider from 0 to 1, step 1)
k_1 = 0 (slider from 0 to 1, step 1)
l_1 = 0 (slider from 0 to 1, step 1)
m_1 = 0 (slider from 0 to 1, step 1)
F_1: (b_1 + (g_1 * c_1), d_1 + (e_1 * g_1))
texte17: "" + (LaTeX[F_1]) + ""
ChampTexte2 = Textfield(g_1)
t = Vector(V, V + (p_1 * u) + (q_1 * v))
P = Midpoint(V, V + (p_1 * u) + (q_1 * v))
ChampTexte3 = Textfield(p_1)
ChampTexte4 = Textfield(q_1)
n_2 = 0 (slider from 0 to 1, step 1)
r_1 = false
i_2 = 0 (slider from -2 to 6, step 1)
s_1 = false
j_2 = 0 (slider from -2 to 5, step 1)
t_1 = true
k_2 = 0 (slider from 0 to 5, step 1)
l_2 = 0 (slider from 0 to 1, step 1)
u_1: abs(p)
texte25: "" + (LaTeX[o]) + " \,x" + (LaTeX[p]) + "\,y=" + (LaTeX[q]) + ""
texte26: "" + (LaTeX[o]) + "\,x+" + (LaTeX[u_1]) + "\,y=" + (LaTeX[q]) + ""
G_1 = Point(f_1)
m_2 = 0 (slider from 0 to 2, step 1)
n_3 = 0 (slider from 0 to 1, step 1)
texte37: "" + (LaTeX[o]) + "\,x+" + (LaTeX[u_1]) + "\,y=" + (LaTeX[q]) + ""
texte38: "" + (LaTeX[o]) + "\,x" + (LaTeX[p]) + "\,y=" + (LaTeX[q]) + ""
l2 = Sequence(Line[E + (k * u), v], k, -20, 20)
l1 = Sequence(Line[E + (k * v), u], k, -20, 20)
o_1 = 0 (slider from -10 to 10, step 0.1)
v_1 = 0 (slider from -10 to 10, step 0.1)
ChampTexte17 = Textfield(o_1)
ChampTexte18 = Textfield(v_1)
i_3 = 0 (slider from 0 to 1, step 1)
H_1 = (-27.544365566770267, 6.621397336472281)
w_1 = Vector(H_1, H_1 + (o_1 * u) + (v_1 * v))
texte40: "\left(\begin{array}{} " + (LaTeX[o_1]) + " \\ " + (LaTeX[v_1]) + " \end{array} \right)"
I_1 = Midpoint(H_1, H_1 + (o_1 * u) + (v_1 * v))
a_2(x, y) = 0
b_2(x, y) = 0
J_1 = (-6.04698605076597, 5.151521867850333)
ChampTexte19 = Textfield(a_2)
ChampTexte20 = Textfield(b_2)
K_1: (m1^(-1) * (J_1 - E))
L_1: E + (a_2(x(K_1), y(K_1)) * u) + (b_2(x(K_1), y(K_1)) * v)
M_1 = (15.506121098969059, 5.603747277149774)
c_2(y) = y > y(M_1)
N_1 = (16.76, 3.8)
texte42: "\left\{\begin{array}{} x'=" + (LaTeX[a_2]) + "\\ y'=" + (LaTeX[b_2]) + "  \end{array}\right. "
m2: {{a_2(1, 0) - a_2(0, 0), a_2(0, 1) - a_2(0, 0)}, {b_2(1, 0) - b_2(0, 0), b_2(0, 1) - b_2(0, 0)}}
m3: {{a_2(0, 0)}, {b_2(0, 0)}}
texte43: "\left(\begin{array}{} x' \\ y'  \end{array} \right)=" + (LaTeX[m2]) + "\left(\begin{array}{} x \\ y  \end{array}\right) +" + (LaTeX[m3]) + ""
j_3 = 1 (slider from 0 to 3, step 1)
k_3 = 0 (slider from 0 to 2, step 1)
O_1 = (11.66, 2.74)
ChampTexte21 = Textfield(e)
ChampTexte22 = Textfield(f)
ChampTexte23 = Textfield(α)
l_3 = 0 (slider from 0 to 1, step 1)
d_2 = 0 (slider from -10 to 10, step 0.1)
e_2 = 0 (slider from -10 to 10, step 0.1)
ChampTexte24 = Textfield(d_2)
ChampTexte25 = Textfield(e_2)
P_1 = (-29.43387245142836, 6.565015001956305)
u_2 = Vector(P_1, P_1 + (d_2 * u) + (e_2 * v))
Q_1 = Midpoint(P_1, P_1 + (d_2 * u) + (e_2 * v))
texte46: "\left(\begin{array}{}" + (LaTeX[d_2]) + "   \\ " + (LaTeX[e_2]) + "  \end{array} \right)"
texte10: "\left(\begin{array}{} " + (LaTeX[p_1]) + "  \\  " + (LaTeX[q_1]) + " \end{array} \right)"
m_3 = 0 (slider from 0 to 1, step 1)
f_2 = 0 (slider from -10 to 10, step 0.1)
g_2 = 0 (slider from -10 to 10, step 0.1)
R_1 = (-28.178802876689687, 1.8870403391849269)
v_2 = Vector(R_1, R_1 + (f_2 * u) + (g_2 * v))
ChampTexte26 = Textfield(f_2)
ChampTexte27 = Textfield(g_2)
S_1 = Midpoint(R_1, R_1 + (f_2 * u) + (g_2 * v))
texte47: "\left(\begin{array}{} " + (LaTeX[f_2]) + "   \\  " + (LaTeX[g_2]) + "  \end{array} \right)"
n_4 = 0 (slider from 0 to 1, step 1)
h_2 = 0 (slider from -10 to 10, step 0.1)
o_2 = 0 (slider from -10 to 10, step 0.1)
T_1 = (-34.181784076868205, 5.6566938614956905)
w_2 = Vector(T_1, T_1 + (h_2 * u) + (o_2 * v))
ChampTexte28 = Textfield(h_2)
ChampTexte29 = Textfield(o_2)
U_1 = Midpoint(T_1, T_1 + (h_2 * u) + (o_2 * v))
texte48: "\left(\begin{array}{}  " + (LaTeX[h_2]) + "   \\   " + (LaTeX[o_2]) + "  \end{array} \right)"
V_1 = (-17.57470102551734, 9.109421133877285)
m4: m1^(-1)
W_1: (m4 * Vector[E, V_1])
texte49: "" + (LaTeX[W_1]) + ""
Z_1 = (-18.42765757359459, 6.927174727078483)
A_2 = (-14.65834834030537, 4.162037114321271)
p_2 = Vector(Z_1, A_2)
B_2 = Midpoint(Z_1, A_2)
C_2: (m4 * p_2)
q_2: x(C_2)
r_2: y(C_2)
texte50: "\left(\begin{array}{}  " + (LaTeX[q_2]) + "  \\  " + (LaTeX[r_2]) + "  \end{array} \right)"
texte13: "C" + (LaTeX[T]) + ""
s_2 = 0 (slider from -10 to 10, step 0.1)
t_2 = 0 (slider from -10 to 10, step 0.1)
a_3 = 0 (slider from -30 to 30, step 0.1)
i_4 = 0 (slider from 0 to 1, step 1)
ChampTexte30 = Textfield(s_2)
ChampTexte31 = Textfield(t_2)
ChampTexte32 = Textfield(a_3)
b_3: s_2^(2) + t_2^(2)
c_3 = If(b_3 ≠ 0, ((s_2 * a_3)) / b_3)
d_3 = If(b_3 ≠ 0, ((t_2 * a_3)) / b_3)
f_3 = If(b_3 ≠ 0, Line[E + (c_3 * u) + (d_3 * v), Vector[((-t_2) * u) + (s_2 * v)]])
e_3 = 0 (slider from -10 to 10, step 0.1)
g_3 = 0 (slider from -10 to 10, step 0.1)
h_3 = 0 (slider from -30 to 30, step 0.1)
j_4 = 0 (slider from 0 to 1, step 1)
ChampTexte33 = Textfield(e_3)
ChampTexte34 = Textfield(g_3)
ChampTexte35 = Textfield(h_3)
o_3: e_3^(2) + g_3^(2)
p_3 = If(o_3 ≠ 0, ((e_3 * h_3)) / o_3)
q_3 = If(o_3 ≠ 0, ((g_3 * h_3)) / o_3)
r_3 = If(o_3 ≠ 0, Line[E + (p_3 * u) + (q_3 * v), Vector[((-g_3) * u) + (e_3 * v)]])
s_3 = 0 (slider from -10 to 10, step 0.1)
t_3 = 0 (slider from -10 to 10, step 0.1)
u_3 = 0 (slider from -10 to 10, step 0.1)
v_3 = 0 (slider from -10 to 10, step 0.1)
ChampTexte36 = Textfield(s_3)
ChampTexte37 = Textfield(t_3)
ChampTexte38 = Textfield(u_3)
ChampTexte39 = Textfield(v_3)
f_4 = If(t_3^(2) + v_3^(2) ≠ 0, Line[E + (s_3 * u) + (u_3 * v), Vector[(t_3 * u) + (v_3 * v)]])
k_4 = 0 (slider from 0 to 2, step 1)
w_3 = 0.75 (slider from -5 to 5, step 0.05)
ChampTexte40 = Textfield(w_3)
D_2: (s_3 + (t_3 * w_3), u_3 + (v_3 * w_3))
E_2: E + (x(D_2) * u) + (y(D_2) * v)
texte64: "" + (LaTeX[D_2]) + ""
texte6: "A" + (LaTeX[N]) + ""
texte12: "B" + (LaTeX[S]) + ""
t1, g_4, h_4, o_4 = Polygon(B_1, O, A_1)
l_4 = OrthogonalLine(O, o_4)
m_4 = OrthogonalLine(A_1, g_4)
p_4 = OrthogonalLine(B_1, h_4)
n_5 = 2 (slider from 0 to 5, step 1)
a_4 = false
q_4 = AngularBisector(A_1, O, B_1)
r_4 = AngularBisector(O, B_1, A_1)
s_4 = AngularBisector(O, A_1, B_1)
F_2 = Intersect(r_4, q_4)
t_4 = OrthogonalLine(F_2, o_4)
G_2 = Intersect(t_4, o_4)
c_4 = Circle(F_2, G_2)
i_5 = 1 (slider from 0 to 1, step 1)
b_4 = LineBisector(O, A_1)
d_4 = LineBisector(B_1, A_1)
e_4 = LineBisector(O, B_1)
H_2 = Midpoint(O, A_1)
I_2 = Midpoint(B_1, A_1)
J_2 = Midpoint(O, B_1)
f_5 = Line(B_1, H_2)
g_5 = Line(O, I_2)
h_5 = Line(J_2, A_1)
c_5 = Circle(B_1, O, A_1)
j_5 = 0 (slider from 0 to 1, step 1)