直線的截距式
Author: 藍邦偉  老師
Date: 15 1 月 2013

$A%v$

$B%v$

$ 截距式 $
$若a,b為非\;0\;實數，\;通過平面上$
$兩點A(a,0)與B(0,b)的直線方$
$程式為\;L:\frac{x}{a}+\frac{y}{b}=1$

$ 設P(x,y)在L上 $
$∵m_{\overline{AP}}=m_{\overline{AB}}$
$∴\frac{y-0}{x-a}=\frac{b-0}{0-a}$
$⇒-ay=bx-ab$
$⇒bx+ay=ab⇒$
$\frac{x}{a}+\frac{y}{b}=1$

C = (4.056608000000028, 0.5557979999999991)
listB = Sequence((0, k), k, ceil(y(Corner[1])), floor(y(Corner[3])))
Q_2: 0.33 * Corner[2] + 0.67 * Corner[1]
listA = Sequence((k, 0), k, ceil(x(Q_2)), floor(x(Corner[3])))
A = Point(listA)
B = Point(listB)
a_1 = Line(A, B)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
Q_3: (x(Q_2), y(Corner[3]))
poly1, c, q_2, q_3, d = Polygon(Corner[1], Q_2, Q_3, Corner[4])
D = (2.42, 2.22)
a: x(A)
b: y(B)
text2: "$通過A" + (LaTeX[A]) + ",與B" + (LaTeX[B]) + "兩點的直線$
$也就是\;x\;截距為\;" + (LaTeX[x(A)]) + ",\;y\;截距為\;" + (LaTeX[y(B)]) + "\;的$
$直線方程式為\; " + (LaTeX[If[x(A) ≟ x(B), "L:\;x=0", If[y(A) ≟ y(B), "L:\;y=0", "L:\; \frac{ x }{" + (x(A)) + "}+ \frac{ y }{" + (y(B)) + " }=1"]]]) + " $
$⇒" + (LaTeX[If[x(A) ≟ x(B), "L:\;x=0", If[y(A) ≟ y(B), "L:\;y=0", "L:\; " + b + "x" + (If[a > 0, "+" + a, "-" + (-a)]) + ("y=" + (a * b))]]]) + "$"