A rotation can be thought of as a turn.

• Pre-image Z is Interactive button. Assistance may be required. ___?___ reflected over line l.
• Image Z' is Interactive button. Assistance may be required. ___?___ reflected over line m.

• Lines l and m  Interactive button. Assistance may be required. ___?___ intersect at one point.
• The pre-image Z was reflected two times.

• The pre-image Z is reflected twice creating a Interactive button. Assistance may be required. ___?___ rotation to image Z''.
• Rotational symmetry occurs when a pre-mage is reflected twice over intersecting lines, creating an image Interactive button. Assistance may be required. ___?___ rotated from the pre-image.

Pause and Reflect

You just generated a translation by reflecting a figure across two lines, then you generated a rotation by reflecting a figure across two lines. What attribute of the two lines will determine if the double-reflection generates a translation or a rotation? (Hint: look at the relationship between the two lines.)

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Check Your Answer

If the two lines are parallel, then the result will be a translation. If the two lines are not parallel, but intersect, the result will be a rotation.

For the two lines that generate a rotation, how does the point of intersection compare to the center of rotation? Do you think that is the case for every double-reflection that generates a rotation? How could you test your conjecture?

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Check Your Answer

The point of intersection of the two lines of reflection coincides with the center of rotation. This is true every time, and could be tested using dynamic geometry software or patty paper for several rotations that are performed in this manner.