Google ClassroomGoogle Classroom
GeoGebraGeoGebra Classroom
GeoGebra

三角形的变换与矩阵演示 iShow

Author:i景然, Simona Riva
Drag the vertices of the given triangle and observe how the coordinates matrix changes accordingly. Choose a predefined transformation or create your custom one using the appearing sliders. The coordinates of the transformed triangle can be obtained by multiplying the transformation matrix by the given triangle's coordinates matrix. 拖动给定三角形的顶点，观察坐标矩阵如何相应变化。 选择预定义的变换，或者使用出现的滑块创建自定义变换。 变换后的三角形坐标可以通过将变换矩阵乘以给定三角形的坐标矩阵得到。

Ready, Set, Practice!

Given the transformation matrix , that maps , write the equations of the transformation, then find the images of the points and . Use the app above to check your results, by selecting the Custom option and setting the matrix using the displayed sliders. 给定变换矩阵 ，映射 ，写出变换方程，然后求点和的像。 使用上方应用查看结果，选择自定义选项，并使用显示的滑块设置矩阵。

Select Dilation from the list of transformations in the app above. Observe the measures of the areas displayed, and how they change when you drag the slider. In particular, check the values obtained when and . What is the relationship between the areas of the given triangle and its image? Does this relationship depend on the dilation ratio ? 从上方应用中的变换列表中选择 “膨胀 ”。 观察显示区域的测量值，以及拖动滑块时它们的变化。 特别地，检查当 和 时得到的值。 给定三角形的面积与其图像之间的关系是什么？ 这种关系是否取决于膨胀比？

Select Dilation from the list of transformations in the app above, and set the ratio . Describe the relative position of the given triangle and its image. Observe the transformation matrix. Now, without modifying the given triangle, select Rotation, and apply a 180° rotation to the given triangle. What do you notice? Can you generalize this? 从上方应用中的变换列表中选择 Dilation，并设置比例 。 描述给定三角形及其图像的相对位置。 观察变换矩阵。 现在，不修改给定的三角形，选择旋转 ，并对给定三角形进行 180°旋转。 你注意到了什么？你能概括一下吗？

#20260728 a11=0 a12=0 a21=0 a22=0 a11c=a11 a12c=a12 a21c=a21 a22c=a21 T={{a11c,a12c},{a21c,a22c}} ratio=滑动条(-2,2,0.1) #$k = %v$ θ=滑动条(0,2pi,0.1) scelte={"$\text{-- 选择一种变换 -- }{{SSR}}quot;,"$\text{自定义变换 }{{SSR}}quot;,"$\text{关于 \(x\)轴对称(反射) }{{SSR}}quot;,"$\text{关于\(y\)轴对称(反射) }{{SSR}}quot;,"$\text{位似变换 }{{SSR}}quot;,"$\text{绕\(O\)旋转 }{{SSR}}quot;,"$\text{斜切 \(x\) }{{SSR}}quot;,"$\text{斜切 \(y\) }{{SSR}}quot;} is=选定索引(scelte) 变更时的脚本 赋值(θ,0) 赋值(a11,如果(is==3 || is>=7,1,is==4,-1,is==5,ratio,is==6,cos(θ),is==1,0,a11)) 赋值(a12,如果(3<=is<=5 || is==8,0,is==6,-sin(θ),is==7,ratio,is==1,0,a12)) 赋值(a21,如果(3<=is<=5 || is==7,0,is==6,sin(θ),is==8,ratio,is==1,0,a21)) 赋值(a22,如果(is==3,-1,is==4 || is>=7,1,is==5,ratio,is==6,cos(θ),is==1,0,a22)) 设置颜色(a11c,如果(is==2,1,3<=is<=5,204/255,37/255),如果(is==2,87/255,3<=is<=5,0,37/255),如果(is==2,34/255,3<=is<=5,76/255,37/255)) 设置颜色(a12c,如果(is==2,41/255,is==7,204/255,37/255),如果(is==2,128/255,is==7,0,37/255),如果(is==2,185/255,is==7,76/255,37/255)) 设置颜色(a21c,如果(is==2,80/255,37/255),如果(is==2,197/255,37/255),如果(is==2,183/255,37/255)) 设置颜色(a22c,如果(is==2,76/255,3<=is<=5,204/255,37/255),如果(is==2,175/255,3<=is<=5,0,37/255),如果(is==2,80/255,3<=is<=5,76/255,37/255)) CM={{x(A),x(B),x(C)},{y(A),y(B),y(C)}} CM'=T CM hideCoord=false 变更时的脚本 设置标注(A,如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) 设置标注(B,如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) 设置标注(C,如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) 设置标注(A',如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) 设置标注(B',如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) 设置标注(C',如果(%0,"$\footnotesize{%n}{{SSR}}quot;,"$\footnotesize{%n=%v}{{SSR}}quot;)) peep: x>-8.3 #白色，底层 all0=A'≟B'≟C'≟(0,0) ∨ is≟6 ∧ θ≟0 poli1Sid=poli1 poli2Sid=poli1' givenCoords="\text{\underline{坐标矩阵}: } \textcolor{#007b61}{" + (公式文本(公式文本(CM, true, true))) + "}" textRapp="\text{" + (公式文本(如果(is ≠ 7, "缩放", "xieqie"))) + " 系数(因子)}" testo1="\text\underline{变换矩阵}\\\\ T=" + (公式文本(表格文本({{a11c, a12c}, {a21c, a22c}}, "()c"))) + " →" + (公式文本(表格文本({{"x'=" 多项式函数(row1)}, {"y'=" 多项式函数(row2)}}, "{h"))) + " \\\\\det(T)=" + (公式文本(行列式(T))) + "" testo3= testo3="\text{面积A\((ABC)=" + (公式文本(面积(poli1))) + "\)\\面积A\((A'B'C')=" + (公式文本(面积(poli1'))) + "\)}"
20260505 修改自：Simona Riva — 2025年3月23日 - 下午6:44 的 Transformations of Triangles and Matrices – GeoGebra
系列： 矩阵与线性变换演示 iShow – GeoGebra 三角形的变换与矩阵演示 iShow – GeoGebra

New Resources

Discover Resources

Discover Topics