Homothetie
Author: Gilles Coulombe

Cliquer et glisser l'un ou l'autre des points A-B-C ou O, ou la figure ABC

A = (0.8630412206850249, -2.165351055078413)
B = (1.2472332586928703, -8.42219281692049)
C = (4.238442697468244, -4.854695321133341)
poly1, c, a, b = Polygon(A, B, C)
O = (15.023262050117067, -4.168638110405043)
A' = Dilate(A, 2, O)
B' = Dilate(B, 2, O)
C' = Dilate(C, 2, O)
poly1', c', a', b' = Polygon(A', B', C')
d = Segment(O, A')
e = Segment(O, C')
f = Segment(O, B')
g = Segment(O, A)
q: d / g
texte1: "k = OA' / OA = \frac{" + (LaTeX[d]) + "}{" + (LaTeX[g]) + "} = " + (LaTeX[q]) + ""
texte2: "OA = " + g + ""
D = Midpoint(O, A)
texte3: "OA' = " + d + ""
A_1 = (-4, 1.92)
O_1 = (-11.52, -1.56)
g_1 = Segment(O_1, A_1)
D_1 = Midpoint(O_1, A_1)
A'_1 = Dilate(A, -0.5, O)
B'_1 = Dilate(B, -0.5, O)
C'_1 = Dilate(C, -0.5, O)
poly1'_1, c'_1, a'_1, b'_1 = Polygon(A'_1, B'_1, C'_1)
h = Segment(O, B'_1)
i = Segment(O, C'_1)
j = Segment(O, A'_1)
texte4: "OA'_1 = - " + j + ""
E = Midpoint(A'_1, O)
r: j / g
s: c' / c
texte6: "Rapport côtés = A'B' / AB = \frac{" + (LaTeX[c']) + "}{" + (LaTeX[c]) + "} = " + (LaTeX[s]) + ""
texte7: "Rapport côtés = A'C' / AC = \frac{" + (LaTeX[b']) + "}{" + (LaTeX[b]) + "} =  " + (LaTeX[s]) + ""
texte8: "Rapport côtés = B' C'/ BC = \frac{" + (LaTeX[a']) + "}{" + (LaTeX[a]) + "} =  " + (LaTeX[s]) + ""
texte9: "Rapport côtés = A'_1B'_1 / AB = \frac{" + (LaTeX[c'_1]) + "}{" + (LaTeX[c]) + "} =  " + (LaTeX[r]) + ""
texte10: "Rapport côtés = A'_1C'_1 / AC = \frac{" + (LaTeX[b'_1]) + "}{" + (LaTeX[b]) + "} =   " + (LaTeX[r]) + ""
texte11: "Rapport côtés = B'_1C'_1 / BC = \frac{" + (LaTeX[a'_1]) + "}{" + (LaTeX[a]) + "} =  " + (LaTeX[r]) + " "
texte5: "k = OA'_1 / OA =  \frac{-" + (LaTeX[j]) + "}{" + (LaTeX[g]) + "} = - " + (LaTeX[r]) + ""