投影點與對稱點
Author: 藍邦偉  老師
Date: 17 1 月 2013

$A$

$B$

$P$

$P'$

投影點與對稱點

$H$

A_0 = (1.04, -0.56)
A = DynamicCoordinates(A_0, floor(x(A_0)), floor(y(A_0)))
B_0 = (6.44, 1.98)
B = DynamicCoordinates(B_0, floor(x(B_0)), floor(y(B_0)))
b: y(A) - y(B)
L = Line(A, B)
P_0 = (3.78, 5.22)
P = DynamicCoordinates(P_0, floor(x(P_0)), floor(y(P_0)))
P' = Mirror(P, L)
c = Segment(P, P')
C = (6.68, -0.28)
A_1 = (1.66, 3.24)
P_5 = (6, 4)
M: 0.5 * A + 0.5 * B
O: 0.5 * (Corner[1] + Corner[3])
P_1: (x(Corner[1]), y(O))
P_2: (x(Corner[2]), y(O))
P_3: (x(O), y(Corner[2]))
P_4: (x(O), y(Corner[3]))
v = Vector(P_3, P_4)
H = Intersect(c, L)
α = Angle(B, H, P)
Q_2: 0.3 * Corner[2] + 0.7 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly1, a_x, q_2, q_3, a_r = Polygon(Corner[1], Q_2, Q_3, Corner[4])
a: x(A) - x(B)
g = GCD(abs(a), abs(b))
l: (a / g, b / g)
u: (b / g, (-a) / g)
h: x(P)
k: y(P)
a_0: a / g
b_0: b / g
d0: x(L)
e0: y(L)
f0: z(L)
g0 = GCD({abs(d0), abs(e0), abs(f0)})
d = If(d0 > 0, d0 / g, If[d0 < 0, (-d0) / g, 0])
e = If(d0 > 0, e0 / g, If[d0 < 0, (-e0) / g, 0])
f = If(d0 > 0, f0 / g, If[d0 < 0, (-f0) / g, 0])
text1: "$ 已知直線L:" + (LaTeX[If[d ≟ 0, "", If[d ≟ 1, "x", d + "x"]]]) + "" + (LaTeX[If[e ≟ 0, "", If[e ≟ 1, "+y", If[e ≟ -1, "-y", If[e > 0, "+" + e + "y", If[e < 0, "-" + (-e) + "y"]]]]]]) + "" + (LaTeX[If[f ≟ 0, "", If[f > 0, "+" + f, If[f < 0, "-" + (-f)]]]]) + "=0與$
$其外一點P" + (LaTeX[P]) + "，\;試求P\;關於$
$L\;的投影點H與對稱點P'$"
text3: "$ 設H(" + (LaTeX[If[h ≟ 0, "", "" + h]]) + "" + (LaTeX[If[a_0 ≟ 0, "", If[a_0 ≟ 1, "+t", If[a_0 ≟ -1, "-t", If[a_0 > 0, "+" + a_0 + "t", If[a_0 < 0, "-" + (-a_0) + "t"]]]]]]) + "," + (LaTeX[If[k ≟ 0, "", "" + k]]) + "" + (LaTeX[If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t", If[b_0 ≟ -1, "-t", If[b_0 > 0, "+" + b_0 + "t", If[b_0 < 0, "-" + (-b_0) + "t"]]]]]]) + ") $
$\;\;\;\;\;\;\;\;\;\;\;∈L:" + (LaTeX[If[d ≟ 0, "", If[d ≟ 1, "x", d + "x"]]]) + "" + (LaTeX[If[e ≟ 0, "", If[e ≟ 1, "+y", If[e ≟ -1, "-y", If[e > 0, "+" + e + "y", If[e < 0, "-" + (-e) + "y"]]]]]]) + "" + (LaTeX[If[f ≟ 0, "", If[f > 0, "+" + f, If[f < 0, "-" + (-f)]]]]) + "=0$"
text2: "$ ⇒ " + (LaTeX[If[d ≟ 0, "", If[d ≠ 0, d + "(" + h + (If[a_0 ≟ 0, "", If[a_0 ≟ 1, "+t", If[a_0 ≟ -1, "-t", If[a_0 > 0, "+" + a_0 + "t", If[a_0 < 0, "-" + (-a_0) + "t)"]]]]]), "" + d]]]) + "" + (LaTeX[If[e ≟ 0, "", If[e ≟ 1, "(" + (If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t", If[b_0 ≟ -1, "-t)", If[b_0 > 0, "+" + b_0 + "t)", If[b_0 < 0, "-" + (-b_0) + "t)"]]]]]), If[e ≟ -1, "(" * If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t)", If[b_0 ≟ -1, "-t)", If[b_0 > 0, "+" + b_0 + "t)", If[b_0 < 0, "-" + (-b_0) + "t)"]]]]], If[e > 0, "+(" + e + (If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t)", If[b_0 ≟ -1, "-t)", If[b_0 > 0, "+" + b_0 + "t)", If[b_0 < 0, "-" + (-b_0) + "t)"]]]]] * If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t)", If[b_0 ≟ -1, "-t", If[b_0 > 0, "+" + b_0 + "t)", If[b_0 < 0, "-" + (-b_0) + "t)"]]]]]), If[e < 0, "-(" + (-e) + (If[b_0 ≟ 0, "", If[b_0 ≟ 1, "+t", If[b_0 ≟ -1, "-t)", If[b_0 > 0, "+" + b_0 + "t)", If[b_0 < 0, "-" + (-b_0) + "t)"]]]]])]]]]]]) + "" + (LaTeX[If[f ≟ 0, "", If[f > 0, "+" + f, If[f < 0, "-" + (-f)]]]]) + "=0$"