平移
Author: 藍邦偉  老師

A(x,y)

(h,k)

A'(x',y')

點的平移

圓的平移

拋物線的平移

橢圓的平移

\left[\begin{array}{cc} x' \ y' \ \end{array}\right]=\left[\begin{array}{rr} x\y \ \end{array}\right]+\left[\begin{array}{cc} h \k \ \end{array}\right]=\left[\begin{array}{rr} x+h \ y+k\ \end{array}\right]

將C:x²+y²+dx+ey+f=0沿 \vec{ a }平移後得新方程式 

C':x'²+y'²+d'x'+e'y'+f'=0

\left[\begin{array}{rr} x' \ y' \ \end{array}\right]=\left[\begin{array}{rr} x+h \ y+k \ \end{array}\right]

\left[\begin{array}{cc} x \ y \ \end{array}\right]=\left[\begin{array}{cc} x'-h \ y'-k \ \end{array}\right]代入，得

C':(x-h)²+(y-k)²+d(x-h)+e(y-k)+f=0

將A(x,y)沿 \vec{ a  }=(h,k)平移後得點A'(x',y') 

拋物線Γ：y=ax²+bx+c或x=ay²+by+c沿 \vec{ a }=(h,k)平移 

Γ'：(y'-h)=a(x'-k)²+b(x'-k)+c或x'-h=a(y'-k)²+b(y'-k)+c

橢圓Γ:ax²+cy²+dx+ey+f=0沿 \vec{ a }=(h,k) 平移

橢圓Γ':a(x'-h)²+c(y'-h)²+d(x'-h)+e(y'-h)+f=0

平移

u = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
v = Vector((0.0, y(Corner[1.0])), (0.0, y(Corner[3.0])))
A = (1.42, 2.468000000000001)
B = (3.22, -0.14)
C = (7.5600000000000005, 2.048000000000001)
a = Vector(B, C)
D = (0, 0)
c = Circle(D, 2.0)
A' = Translate(A, a)
c' = Translate(c, a)
b = false
e = false
F = (3.36, 2.468000000000001)
E = (-0.98, -1.8719999999999994)
G = (-1, 3.928000000000001)
d = Line(G, E)
f = Parabola(F, d)
f' = Translate(f, a)
g = false
F_1 = (0.64, 1.9680000000000006)
F_2 = (4.04, 1.9080000000000008)
J = (2.72, 0.6880000000000007)
h = Ellipse(F_1, F_2, J)
h' = Translate(h, a)
i = false
O = (0, 0)
w = Vector(O, A)
z = Vector(O, A')
n = 0 (slider from 0 to 1, step 1)
m = 0 (slider from 0 to 1, step 1)
k = 0 (slider from 0 to 1, step 1)