Trisección de un segmento
Trisección de un segmento
Razón AM a MB Razón AN a NB
a) rm = AM/MB b) rn = AN/NB
rm = x/(x+x) rn = (x+x)/x
rm = x/2x rn = 2x/x
rm = 1/2 rm = 0.5 rn = 2
rm = x/(x+x) rn = (x+x)/x
rm = x/2x rn = 2x/x
rm = 1/2 rm = 0.5 rn = 2
El segmento visto desde el plano Cartesiano
Las formulas son
Caso I
xm = (x1 + rx2)/(1 + r) ym = (y1+ry2)/(1 + r)
xm = (0 + (0.5)(4))/(1 + 0.5) ym = (- 3 + 0.5(7))/(1 + 0.5)
xm = (0 + 2)/1.5 ym = (- 3 + 3.5)/(1.5)
xm = 2/1.5 ym = 0.5/1.5
xm = 1.33 ym = 0.33
caso II
caso II
Xn = (x1 + rx2)/(1 + r) yn = (y1+ry2)/(1 + r)
xn = (0 + (2)(4))/(1 + 2) yn = (- 3 + 2(7))/(1 + 2)
xn = (0+8)/3 yn = (- 3 + 14)/3
xn=8/3 yn = 11/3
xn=2.66 yn = 3.66
Los nuevos puntos son: M(1.33, 0.33) y N(2.66, 3.66)
Otra manera de comprobar que la distancia entre cada pareja de puntos tiene aproximadamente iguales longitudes.
AM = √ (x2 – x1)2 + (y2 – y1)2 MN = √ (x2 – x1)2 + (y2 – y1)2
AM = √ (1.33 – 0)2 + (0.33 – (-3))2 MN = √ (2.66 – 1.33)2 + (3.66 –0.33)2
AM = √ (1.33 – 0)2 + (0.33 – (-3))2 MN = √ (2.66 – 1.33)2 + (3.66 –0.33)2
AM = √ (1.33)2 + (0.33 + 3)2 MN =√ (1.33)2 + (3.33)2
AM = √ 1.77 + (3.33)2 MN = √ 1.77 + 11.09
AM = √ 1.77 + 11.09 MN = √ 12.86
AM = √ 12.86 MN = 3.5
AM = 3.5
NB = √ (x2 – x1)2 + (y2 - y1)2 NB = √ 1.7 + 11.15
NB = √ (4 – 2.66)2 + (7 – 3.66)2 NB = √ 12.85
NB = √ (1.34)2 + (3.34)2 NB = 3.5
Por tanto AM ≈ MN ≈ NB