[img]data:image/png;base64,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[/img]
[size=150]For each diagram, find a sequence of translations and rotations that take the original figure to the image, so that if done physically, the figure would not touch any of the solid obstacles and would not leave the diagram. Test your sequence by drawing the image of each step.[/size]
Describe a sequence of translations, rotations, and reflections that will take parallelogram [math]ABCD[/math] to parallelogram [math]A'B'C'D'[/math].
Describe a sequence of translations, rotations, and reflections that will take parallelogram [math]ABCD[/math] to parallelogram [math]A'B'C'D'[/math].
[size=150][size=100]In this unit, we have been focusing on rigid transformations in two dimensions. By thinking carefully about precise definitions, we can extend many of these ideas into three dimensions. How could you define rotations, reflections, and translations in three dimensions?[/size][/size]