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GeoGebra

Transformations of Triangles and Matrices

Autor: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.

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.

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 ?

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?

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