2D 座標架
Author: 藍邦偉  老師

$ O $

$Step=%v$

$B$

$A$

$ 分點公式(1) $

$n=%v$

$m=%v$

$P$

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.67 * Corner[1] + 0.33 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
s = 0 (slider from 0 to 3, step 1)
t1 = 0 (slider from 0 to 1, step 0.01)
t2 = 0 (slider from 0 to 1, step 0.01)
t3 = 0 (slider from 0 to 1, step 0.01)
t4 = 0 (slider from 0 to 1, step 0.01)
t5 = 0 (slider from 0 to 1, step 0.01)
B_0 = (-0.5405660522856218, 4.510711025603892)
B = DynamicCoordinates(B_0, floor(x(B_0)), floor(y(B_0)))
A_0 = (6, 3)
A = DynamicCoordinates(A_0, floor(x(A_0)), floor(y(A_0)))
a1: x(A)
a2: y(A)
b1: x(B)
b2: y(B)
n = 2 (slider from 1 to 10, step 1)
m = 4 (slider from 1 to 10, step 1)
g = GCD(m, n)
text0: "$ 已知A" + (LaTeX[If[s ≟ 0, "(x_1,y_1)", "" + A]]) + "," + (LaTeX[If[s ≟ 0, "B(x_2,y_2) ", "" + B]]) + "，\;且P\;在$
$\overline{AB}上，\;若\overline{PA}:\overline{PB}=" + (LaTeX[If[s ≟ 0, "m", "" + (m / g)]]) + ":" + (LaTeX[If[s ≟ 0, "n", "" + (n / g)]]) + ",\;則:$
$\overrightarrow{OP}=" + (LaTeX[If[s ≟ 0, "\frac{n}{m+n}", "" * FractionText[n / (m + n)]]]) + "\;\overrightarrow{OA}+" + (LaTeX[If[s ≟ 0, "\frac{m}{m+n}", "" + (FractionText[m / (m + n)])]]) + "\overrightarrow{OB}$"
P: n / (n + m) * A + m / (n + m) * B
text1: "$ \overrightarrow{OP}=" + (LaTeX[FractionText[n / (m + n)]]) + " \;" + (LaTeX[A]) + "+" + (LaTeX[FractionText[m / (m + n)]]) + "\;" + (LaTeX[B]) + "$"
c: n / (n + m)
d: m / (m + n)
a = Segment(B, A)
u_1 = Vector(O, A)
u_3 = Vector(O, B)
u_2 = Vector(O, P)
A_1: O + t1 * Vector[O, A]
B_1: O + t1 * Vector[O, B]
P_1: O + t1 * Vector[O, P]
v_1 = Vector(O, A_1)
v_2 = Vector(O, P_1)
v_3 = Vector(O, B_1)
list = Sequence(A + j / (m + n) * Vector[A, B], j, 1, m + n)
b = Segment(A, B)
text3_1: "$ =(\;" + (LaTeX[FractionText[c * x(A) + d * x(B)]]) + "\;,\;" + (LaTeX[FractionText[c * y(A) + d * y(B)]]) + "\;) $"
text2_1: "$ =(\;" + (LaTeX[FractionText[c * x(A)]]) + "\;,\;" + (LaTeX[FractionText[c * y(A)]]) + "\;) +(\;" + (LaTeX[FractionText[d * x(B)]]) + "\;,\;" + (LaTeX[FractionText[d * y(B)]]) + "\;)$"