數與數線(9)
Author: 藍邦偉　老師

X

Y

O

A

B

P

Q

∵ΔOAP≈\Delta OBQ

∴\frac{\overline{OA}}{\overline{OB}}=\frac{\overline{OP}}{\overline{OQ}}

⇒\frac{α}{4+\frac{8}{9}}=\frac{7+\frac{36}{99}}{β}

⇒αβ=\frac{44}{9}×\frac{81}{11}=36

又1<α<β<10,α,β∈\mathbb{Z}

$ ⇒α=4,β=9 $

O = (-4.64, -0.64)
v = Vector(O - (1, 0), O + (4.5, 0))
W = (-5.34, -1.08)
a = Line(W, O)
B_1 = Point(a)
u = Vector(W, B_1)
A = Point(v)
B = Point(v)
P = Point(u)
b = Segment(P, A)
c = Line(B, b)
Q = Intersect(c, a)
d = Segment(Q, B)
n = 0 (slider from 0 to 7, step 1)