Lesson 7

Rotation Patterns

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Problem 1

For the figure shown here,

  1. Rotate segment CD 180^\circ around point D.
  2. Rotate segment CD 180^\circ around point E.
  3. Rotate segment CD 180^\circ around point M.
Segment C D with midpoint M and C D rising from left to right. Point E is above M D, slightly left of point D.

 

Solution

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Problem 2

Here is an isosceles right triangle:

Draw these three rotations of triangle ABC together.

  1. Rotate triangle ABC 90 degrees clockwise around A.
  2. Rotate triangle ABC 180 degrees around A.
  3. Rotate triangle ABC 270 degrees clockwise around A.
Right isosceles triangle A B C has horizonatl side A B with point A to the right of B, and has vertical side B C with point C directly above point B.

Solution

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Problem 3

Each graph shows two polygons ABCD and A’B’C’D’. In each case, describe a sequence of transformations that takes ABCD to A’B’C’D’.

  1.  
    Quadrilateral \(A \ B\ C\ D\) and its image quadrilateral \(A\ prime\ B\ prime\ C\ prime\ D\ prime\)  on a coordinate plane, origin \(O\).
  2.  
    Quadrilateral \(A\ B\ C\ D\) and its image quadrilateral \(A\ prime\ B\ prime\ C\ prime\) and \(D\ prime\) on a coordinate plane, origin \(O\).

Solution

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(From Unit 1, Lesson 4.)

Problem 4

Lin says that she can map Polygon A to Polygon B using only reflections. Do you agree with Lin? Explain your reasoning.

Two quadrilaterals polygon A and B on a grid.

Solution

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(From Unit 1, Lesson 3.)