矩阵过渡矩阵演示

几何画板及绘图内容加载中，请稍等……

2016-11-17 03:49

解析几何矩阵

①本范例演示了矩阵在几何变换中的应用，通过矩阵过渡展示了图形的变换过程；②涉及的核心数学概念包括矩阵运算、几何变换、解析几何；③作图要点提炼自构造摘要，使用了PolyLine（多段线）、ApplyMatrix（应用矩阵）、Intersect（交点）、Segment（线段）等GeoGebra命令和对象；④适合高中及以上数学学习者，用于理解矩阵与几何变换的关系，以及解析几何作图方法。

GeoGebra 命令及参数

PolyLine((3.26, 5.2), (3.12, 5.2), (2.2, 5.02), (8.54000000000001, 3.52), (8.54000000000001, 3.62), (8.52000000000001, 3.7), (8.50000000000001, 3.78), (8.46000000000001, 3.86), (8.40000000000001, 3.94), (8.38000000000001, 4), (8.34000000000001, 4.08), (8.30000000000001, 4.14), (8.26000000000001, 4.2), (2.22, 4.94), (8.22000000000001, 4.26), (8.20000000000001, 4.32), (8.14000000000001, 4.36), (8.08000000000001, 4.4), (8.02000000000001, 4.42), (7.94000000000001, 4.46), (7.86000000000001, 4.48), (7.78000000000001, 4.48), (7.70000000000001, 4.48), (7.60000000000001, 4.48), (2.28, 4.9), (7.52000000000001, 4.48), (7.42000000000001, 4.48), (7.30000000000001, 4.48), (7.24000000000001, 4.46), (7.12000000000001, 4.46), (7.00000000000001, 4.46), (6.94000000000001, 4.48), (6.86000000000001, 4.48), (6.80000000000001, 4.52), (6.70000000000001, 4.6), (2.34, 4.86), (6.62000000000001, 4.64), (6.54000000000001, 4.72), (6.48000000000001, 4.78), (6.44000000000001, 4.84), (6.42000000000001, 4.9), (6.36000000000001, 4.94), (6.34000000000001, 5), (6.28000000000001, 5.08), (6.26000000000001, 5.14), (6.22000000000001, 5.22), (2.36, 4.78), (6.20000000000001, 5.28), (6.18000000000001, 5.34), (6.18000000000001, 5.42), (6.14000000000001, 5.54), (6.12000000000001, 5.6), (6.12000000000001, 5.72), (6.10000000000001, 5.82), (6.06000000000001, 5.9), (5.92000000000001, 6), (5.76000000000001, 6.08), (2.42, 4.76), (5.64000000000001, 6.16), (5.54000000000001, 6.24), (5.42000000000001, 6.28), (5.30000000000001, 6.3), (5.22000000000001, 6.34), (5.16000000000001, 6.38), (5.08000000000001, 6.4), (5.00000000000001, 6.44), (4.92000000000001, 6.44), (4.86000000000001, 6.48), (2.46, 4.7), (4.78000000000001, 6.48), (4.72000000000001, 6.5), (4.60000000000001, 6.5), (4.50000000000001, 6.5), (4.40000000000001, 6.5), (4.32000000000001, 6.48), (4.28000000000001, 6.42), (4.20000000000001, 6.38), (4.14000000000001, 6.32), (4.08000000000001, 6.26), (2.54, 4.62), (4.02000000000001, 6.2), (4.00000000000001, 6.12), (3.96000000000001, 6.06), (3.92000000000001, 5.96), (3.90000000000001, 5.88), (3.90000000000001, 5.8), (3.90000000000001, 5.72), (3.90000000000001, 5.64), (3.86000000000001, 5.58), (3.82000000000001, 5.52), (2.62, 4.56), (3.76000000000001, 5.44), (3.72000000000001, 5.38), (3.66000000000001, 5.34), (3.60000000000001, 5.3), (3.52000000000001, 5.3), (3.42000000000001, 5.3), (3.34, 5.28), (3.28, 5.24), (3.26, 5.18), (3.24, 5.12), (2.68, 4.5), true, (2.98, 5.2), (2.74, 4.48), (2.82, 4.38), (2.9, 4.32), (2.92, 4.24), (2.98, 4.16), (3.02, 4.08), (3.04, 4.02), (3.06, 3.92), (3.1, 3.86), (3.14, 3.8), (2.76, 5.2), (3.2, 3.78), (3.22, 3.72), (3.22, 3.62), (3.22, 3.5), (3.22, 3.42), (3.2, 3.26), (3.2, 3.18), (3.18, 3.1), (3.18, 3), (3.18, 2.92), (2.58, 5.2), (3.24, 2.88), (3.3, 2.84), (3.40000000000001, 2.78), (3.48000000000001, 2.74), (3.64000000000001, 2.68), (3.78000000000001, 2.62), (3.96000000000001, 2.56), (4.16000000000001, 2.56), (4.34000000000001, 2.52), (4.40000000000001, 2.5), (2.42, 5.2), (4.48000000000001, 2.5), (4.56000000000001, 2.5), (4.62000000000001, 2.48), (4.72000000000001, 2.48), (4.80000000000001, 2.48), (4.90000000000001, 2.48), (4.98000000000001, 2.48), (5.10000000000001, 2.48), (5.22000000000001, 2.48), (5.28000000000001, 2.5), (2.34, 5.2), (5.34000000000001, 2.52), (5.42000000000001, 2.54), (5.50000000000001, 2.62), (5.56000000000001, 2.64), (5.64000000000001, 2.7), (5.70000000000001, 2.76), (5.80000000000001, 2.82), (5.86000000000001, 2.84), (5.92000000000001, 2.86), (5.98000000000001, 2.88), (2.26, 5.2), (6.10000000000001, 2.88), (6.26000000000001, 2.72), (6.34000000000001, 2.68), (6.42000000000001, 2.56), (6.54000000000001, 2.44), (6.64000000000001, 2.28), (6.76000000000001, 2.2), (6.84000000000001, 2.08), (6.94000000000001, 1.96), (7.02000000000001, 1.92), (2.2, 5.18), (7.12000000000001, 1.86), (7.20000000000001, 1.82), (7.28000000000001, 1.82), (7.38000000000001, 1.82), (7.50000000000001, 1.82), (7.64000000000001, 1.82), (7.80000000000001, 1.86), (7.94000000000001, 1.94), (8.10000000000001, 2.06), (8.22000000000001, 2.18), (2.2, 5.1), (8.34000000000001, 2.32), (8.44000000000001, 2.44), (8.48000000000001, 2.56), (8.48000000000001, 2.7), (8.50000000000001, 2.84), (8.50000000000001, 2.92), (8.54000000000001, 3.08), (8.54000000000001, 3.18), (8.54000000000001, 3.3), (8.54000000000001, 3.42)) → a
ApplyMatrix(B, a) → a'
ApplyMatrix(A, a) → a'_1
ApplyMatrix(C, a) → a'_2
ApplyMatrix(D, a) → a'_3
ApplyMatrix(E, a) → a'_4
Intersect(g, a'_3) → F, G
Intersect(g, a) → H, I
Intersect(f, a) → J, K
Intersect(f, a'_3) → L, M
Segment(F, H) → n
Segment(L, J) → p

AI 绘图提示语参考

画一个由多段线组成的形状，并展示其通过不同矩阵变换后的效果。首先绘制原始形状，然后应用五个不同的矩阵变换，分别得到五个新的形状。接着，找到原始形状和变换后形状与某条参考线的交点，并连接这些交点形成新的线段，最终展示矩阵变换对形状的影响。

以上提示语为根据原始绘图命令整理而来，仅供参考。