IM Geo.1.14 Practice: Defining Rotations

Draw the image of quadrilateral ABCD when rotated 120° counterclockwise around the point D.
There is an equilateral triangle, ABC, inscribed in a circle with center D.
What is the smallest angle you can rotate triangle [math]ABC[/math] around  so that the image of [math]A[/math] is [math]B[/math]?
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[/img][br]Which segment is the image of [math]AB[/math] when rotated [math]90°[/math]counterclockwise around point [math]P[/math]?
The semaphore alphabet is a way to use flags to signal messages. Here's how to signal the letter Q.
[img]data:image/png;base64,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[/img][br]Describe a transformation that would take the right hand flag to the left hand flag.
Here are 2 polygons:
[img]data:image/png;base64,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[/img][br][br]Select [b]all [/b]sequences of translations, rotations, and reflections below that would take polygon [math]P[/math] to polygon [math]Q[/math].[br]
Draw the image of figure ABC when translated by directed line segment u. Label the image of A as A', the image of B as B', and the image of C as C'.
Explain why the line containing [math]AB[/math] is parallel to the line containing [math]A'B'[/math].
There is a sequence of rigid transformations that takes A to A', B to B', and C to C'. The same sequence takes D to D'. Draw and label D':
Close

Information: IM Geo.1.14 Practice: Defining Rotations