領域

２つの一次式の積で表される不等式の領域を描きましょう。

正解

領域変更

赤い点は緑の点の右上に，
青い点は緑の点の左上に
なるようにしてください．

e1(x, y) = ((-1.1)  <  x) ∧ (x  <  1.1) ∧ ((-1.1)  <  y) ∧ (y  <  1.1)
e2(x, y) = (x > 1.1) ∧ (y > 1.1)
e3(x, y) = (x  <  (-1.1)) ∧ (y > 1.1)
ax = Random(-1, 1)
ay = Random(-1, 1)
bx: ax + (Random[1, 2] * 2)
by: ay + (Random[1, 2] * 2) - 1
f1 = Expand(((bx - ax) * (y - ay)) - ((x - ax) * (by - ay)))
cy: ay + (Random[1, 2] * 2)
cx: ax - (Random[1, 2] * 2) + 1
f2 = Expand(((x - cx) * (ay - cy)) - ((ax - cx) * (y - cy)))
n1: (Random[0, 1] * 2) - 1
text1 = If(n1 ≟ 1, "\ge ", "\le ")
n = -1
A = (1, 0)
B = (3, 1)
fa(x, y) = ((x(B) - x(A)) * (y - y(A))) - ((x - x(A)) * (y(B) - y(A)))
C = (0, 2)
fb(x, y) = ((x - x(C)) * (y(A) - y(C))) - ((x(A) - x(C)) * (y - y(C)))
ans1: ax ≟ x(A) ∧ ay ≟ y(A)
ans4: f2(x(C), y(C)) ≟ 0
ans3: f1(x(B), y(B)) ≟ 0
e4(x, y) = ((fa(x, y) * fb(x, y)) * n) ≥ 0
text3: "(" + (LaTeX[f1]) + ")( " + (LaTeX[f2]) + ")" + (LaTeX[text1]) + "0 を表してください．"
ans2: n ≟ n1
ans: ans1 ∧ ans2 ∧ ans3 ∧ ans4