+

+

-

-

Escala

Ángulo

Distancia

Ejercicio

Ejemplo

Otro ejercicio

Ejercicio

Ejemplo

Escribe en las casillas el cociente 
y el resto de la división.

Comprobar

¡ Muy bien !

No es correcto. 
Revisa los cálculos.

Nuevo intento

Selecciona el número de intervalos que hay que tomar en la semirrecta
y mueve el punto P (verde) a la posición correcta.

P

comprobar

¡Muy bien !

No es correcto. Revisa el número de 
intervalos y la posición del punto verde.

Ver construcción paso a paso

Nuevo intento

Reiniciar construcción

Escala

Ángulo

Distancia

esc1 = 4.1 (slider from 2 to 5, step 0.05)
O' = (0, 1)
signo: {-1, 1}
β = 0.6457718232379019 rad (slider from ° to 80°, step °)
den1 = Random(2, 9)
num11: (RandomElement[signo] * ((den1 * Random[1, 4]) + Random[1, den1 - 1]))
num1: abs(num11)
mcd = GCD(num1, den1)
num: num11 / mcd
esc = 4.1 (slider from 1 to 5, step 0.1)
G = If(num ≥ 0, O' - (esc1, 0), O' + (esc1, 0))
G' = Mirror(G, O')
dis1 = 0.9 (slider from 0.5 to 1.5, step 0.05)
E2 = (-2.996363636363636, 1.761818181818183)
a = 17 (slider from -20 to 20, step 1)
b = 7 (slider from 3 to 9, step 1)
absa: abs(a)
texto1: "" + absa + ""
texto2: "" + b + ""
c1 = Div(absa, b)
texto3: "" + c1 + ""
r1 = Mod(absa, b)
texto4: "" + r1 + ""
E1: E2 + (0, 0.6)
s1 = Segment(E1, E2)
E3: E2 + (0.8, 0)
s2_1 = Segment(E2, E3)
texto5: "" + (LaTeX[absa]) + "=" + (LaTeX[b]) + "·" + (LaTeX[c1]) + "+" + (LaTeX[r1]) + ""
texto6: "\frac{" + (LaTeX[absa]) + "}{" + (LaTeX[b]) + "}=" + (LaTeX[c1]) + "+\frac{" + (LaTeX[r1]) + "}{" + (LaTeX[b]) + "}"
O: (0, 0)
A = If(a ≥ 0, O - (esc, 0), O + (esc, 0))
A' = Mirror(A, O)
p = If(a ≥ 0, c1, (-c1))
texto8: "" + p + ""
q = If(a ≥ 0, p + 1, p - 1)
texto9: "" + q + ""
c = Segment(A', A)
semi = Ray(A, A')
α = 1.0821041362364843 rad (slider from 10° to 80°, step 0.017453292519943295)
d = If(a ≥ 0, Ray[Rotate[A, α, A], Rotate[A', α, A]], Ray[Rotate[A, (-α), A], Rotate[A', (-α), A]])
dis = 0.9 (slider from 0.5 to 2, step 0.05)
e = Circle(A, dis)
B = Intersect(e, d)
lista1 = Sequence(A + (i * (B - A)), i, 1, b)
lista2 = Last(lista1)
C = Point(lista2)
f = Segment(A', C)
lista3 = Sequence(A + (i * (A' - A) / b), i, 1, b - 1)
lista4 = Zip(Segment[A, B], A, lista1, B, lista3)
D: A + (r1 * (B - A))
g = Line(D, f)
E = Intersect(g, c)
h = Segment(D, E)
texto10: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}"
F: A + ((b + 1.5) * (B - A))
i = Segment(A, F)
paso = 10 (slider from 0 to 10, step 1)
j = Line(A, A')
texto11: "" + r1 + ""
ejer: 0
den: den1 / mcd
texto15: "Representa\:la\:fracción\:\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den]) + "}"
absnum: abs(num)
texto16: "" + absnum + ""
texto17: "" + den + ""
coci: 0 / 0
rest: 0 / 0
CasillaDeEntrada1 = Textfield(coci)
CasillaDeEntrada2 = Textfield(rest)
texto19: "\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den]) + "}=" + (LaTeX[coci]) + "+\frac{" + (LaTeX[rest]) + "}{" + (LaTeX[den]) + "}"
texto20: "\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den]) + "}=-" + (LaTeX[coci]) + "-\frac{" + (LaTeX[rest]) + "}{" + (LaTeX[den]) + "}"
solcoci = Div(abs(num), den)
solrest = Mod(abs(num), den)
est = 0 (slider from 0 to 2, step 1)
sol1: coci ≟ solcoci ∧ rest ≟ solrest
texto7: "⇒\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "}=-" + (LaTeX[c1]) + "-\frac{" + (LaTeX[r1]) + "}{" + (LaTeX[b]) + "}"
izq = If(num ≥ 0, solcoci, (-solcoci) - 1)
der: izq + 1
texto23: "\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den1]) + "}\:está\:en\:el \:intervalo\:\left [" + (LaTeX[izq]) + " ," + (LaTeX[der]) + " \right ] "
npas = 10 (slider from 2 to 10, step 1)
k = Segment(G', G)
s2 = Ray(G, G')
s3 = If(num ≥ 0, Ray[Rotate[G, β, G], Rotate[G', β, G]], Ray[Rotate[G, (-β), G], Rotate[G', (-β), G]])
r = Circle(G, dis1)
H = Intersect(r, s3, 1)
lista5 = Sequence(G + (i * (H - G)), i, 1, npas)
lista6 = Last(lista5)
S = Point(lista5)
K = Point(lista6)
l = Segment(G', K)
m = Line(S, l)
L = Intersect(m, k)
n = Segment(S, L)
sol2: npas ≟ den ∧ Distance[S, G] ≟ (solrest * Distance[H, G])
o = false
np = If(num ≥ 0, solcoci, (-solcoci))
texto27: "" + np + ""
s = Line(G, G')
ns = If(num ≥ 0, np + 1, np - 1)
texto28: "" + ns + ""
texto29: "Intervalos =" + npas + ""
texto30: "\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den]) + "}"
R = (-4, -2.5)
aciertos = 0 (slider from 0 to 8, step 1)
lista7 = Sequence(Translate[Circle[R, 0.2], Vector[(i * Vector[R, R + (0.5, 0)])]], i, 1, aciertos)