直線的參數式(1)
Author: 藍邦偉  老師
Date: 15 1 月 2013

$P%v$

$%v$

$ 直線的參數式(1) $

$ 通過P\;(\;x_0,y_0\;)\;且方向向量為$
$\vec{L}=(a,b) 的直線方程式為$
$\left\lbrace\begin{array}{ll} x=x_0+at  \ y=y_0+bt \ \end{array}   \right.\ ,t∈\mathbb{R}$

A_0 = (-1, 2)
A = DynamicCoordinates(A_0, floor(x(A_0)), floor(y(A_0)))
A_1 = (2.106, 3.192)
P = DynamicCoordinates(A_1, floor(x(A_1)), floor(y(A_1)))
K_1: (x(Corner[1]), 0)
T_2: (7 * Corner[1] + 3 * Corner[2]) / 10
K_2: (x(Corner[2]), 0)
h: x(P)
a: x(A)
k: y(P)
b: y(A)
u = Vector((0, 0), A)
L = Line(P, u)
T_1 = Corner(1)
T_4 = Corner(4)
T_3: (x(T_2), y(Corner[3]))
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
c = Segment(T_2, T_3)
text8: "$ 通過點P(" + (LaTeX[h]) + "," + (LaTeX[k]) + ") 且方向向量為$
$\vec{L}=(" + (LaTeX[a]) + "," + (LaTeX[b]) + ")的直線方程式為$"
text1: "\left\lbrace\begin{array}{ll} x=" + (LaTeX[If[h ≟ 0, "", "" + h]]) + "" + (LaTeX[If[a ≟ 0, "", If[a ≟ 1, "+t", If[a ≟ -1, "-t", If[a > 0, "+" + a + "t", If[a < 0, "-" + (-a) + "t"]]]]]]) + " \\ y=" + (LaTeX[If[k ≟ 0, "", "" + k]]) + "" + (LaTeX[If[b ≟ 0, "", If[b ≟ 1, "+t", If[b ≟ -1, "-t", If[b > 0, "+" + b + "t", If[b < 0, "-" + (-b) + "t"]]]]]]) + " \\ \end{array}   \right.\ ,t∈\mathbb{R}"
g = GCD(a, b)