分點公式(2)
Author: 藍邦偉  老師

移動A,B兩點與拉竿m,n觀察外分點P的變化

分點公式(2)

P

P

m=

m

,

n=

n

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
A = (2, 3)
B = (-1, 2)
m = 3 (slider from 1 to 10, step 1)
n = 5 (slider from 1 to 10, step 1)
P_2: n / (n - m) * A - m / (n - m) * B
a = Vector(O, A)
b = Vector(O, B)
p = Vector(O, P_2)
文字2: " \overline{ PA }: \overline{ PB }=" + m + ":" + n
c = Segment(A, P_2)
d = Segment(P_2, B)
f = LineBisector(P_2, B)
E = Intersect(f, d)
h = Circle(E, P_2)
e = LineBisector(A, P_2)
C = Intersect(e, c)
g = Circle(C, A)
D = Intersect(g, e, 1)
F = Intersect(h, f, 1)
文字9: " \overline{ PB }: \overline{ BA }=" + n + ":" + (m - n)
文字4: " \vec{ OB } = \frac{ " + n + " }{" + m + " } \vec{ OA }+ \frac{ " + (m - n) + " }{ " + m + "}  \vec{ OP }   "
文字10: " \vec{ OP }=-\frac{" + n + "  }{" + (m - n) + " } \vec{ OA }+ \frac{" + m + "  }{" + (m - n) + "}  \vec{ OB }"
文字5: "=- \frac{" + n + " }{" + (m - n) + " }" + A + "+ \frac{" + m + "  }{" + (m - n) + " }" + B
文字8: "=(" + (FractionText[(-n * x(A) + m * x(B)) / (m - n)]) + "," + (FractionText[(-n * y(A) + m * y(B)) / (m - n)]) + ")"
文字16: " \overline{ PA } : \overline{ PB }= " + m + ":" + n
T_4 = Corner(4)
T_1 = Corner(1)
T_2: 0.7 * Corner[1] + 0.3 * Corner[2]
T_3: 0.7 * Corner[4] + 0.3 * Corner[3]
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
i = Segment(T_2, T_3)
P_1: (-n) / (m - n) * A + m / (m - n) * B
j = Segment(P_1, A)
文字3: "A" + (LaTeX[A]) + ",B" + (LaTeX[B]) + ""
inputBox1 = Textfield(m)
inputBox2 = Textfield(n)
文字12: " \overrightarrow{OA}= \frac{ " + (LaTeX[n - m]) + " }{" + (LaTeX[n]) + " } \overrightarrow{OP}+ \frac{ " + (LaTeX[m]) + " }{" + (LaTeX[n]) + " } \overrightarrow{OB}"
文字11: "⇒ \overline{ PA }:  \overline{ AB }=" + (LaTeX[m]) + ":" + (LaTeX[n - m]) + ""
文字13: "\overrightarrow{OP}= \frac{ " + (LaTeX[n]) + " }{" + (LaTeX[n - m]) + " } \overrightarrow{OA}- \frac{ " + (LaTeX[m]) + " }{" + (LaTeX[n - m]) + " }  \overrightarrow{OB}"
文字14: "= \frac{ " + (LaTeX[n]) + " }{" + (LaTeX[n - m]) + " }" + (LaTeX[A]) + "- \frac{ " + (LaTeX[m]) + " }{" + (LaTeX[n - m]) + " } " + (LaTeX[B]) + ""
文字15: "=(" + (LaTeX[FractionText[(n * x(A) - m * x(B)) / (n - m)]]) + "," + (LaTeX[FractionText[(n * y(A) - m * y(B)) / (n - m)]]) + ")"