变换练习：将矩形映射到矩形

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2016-08-04 00:00

向量变换几何作图

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本范例演示了如何通过几何变换将一个矩形映射到另一个矩形。核心数学概念包括几何变换、线性方程和向量。通过使用GeoGebra命令如Random、Line、Rotate、Translate等，可以构造出变换后的图形。适合初中及以上学生学习几何变换和相关概念。

GeoGebra 命令及参数

Random(1, 359) → p
Line(A, B) → f
OrthogonalLine(A, f) → g
Point(g) → C
Ray(A, C) → i
Point(i) → D
OrthogonalLine(D, i) → j
OrthogonalLine(B, f) → h
Intersect(h, j) → E
Segment(E, D) → m
Midpoint(m) → H
Segment(A, B) → k
Midpoint(k) → I
Midpoint(H, I) → J
Random(-3, 3) → c
Random(-4, 4) → o
Polygon(A, B, E, D) → poly1, a, b, e, d
Segment(B, E) → l
Segment(D, A) → n
Angle(poly1) → α, β, γ, δ
Rotate(A, (p * π / 180), J) → A'
Rotate(B, (p * π / 180), J) → B'
Rotate(E, (p * π / 180), J) → E'
Rotate(D, (p * π / 180), J) → D'
Polygon(A', B', E', D') → poly1', a', b', e', d'
Vector(J, (x(J) + (sqrt(c^(2) + o^(2)) * cos((p * π / 180))), y(J) + (sqrt(c^(2) + o^(2)) * sin((p * π / 180))))) → u
Translate(A', u) → A''
Translate(B', u) → B''
Translate(E', u) → E''
Translate(D', u) → D''
Polygon(A'', B'', E'', D'') → poly1'', a'', b'', e'', d''
Segment(D'', E'') → q
Segment(E'', B'') → r
Segment(B'', A'') → s
Segment(A'', D'') → t