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3-37. Examine the figure graphed on the axes at right. What happens when you rotate this figure about the origin 90°? 45°? 180°? а. By what other angle could the figure at right be rotated so that the shape does not appear to change? b. What shape will stay the same no matter how many degrees it is rotated? с.

3-37. Examine the figure graphed on the axes at right. What happens when you rotate this figure about the origin 90°? 45°? 180°? а. By what other angle could the figure at right be rotated so that the shape does not appear to change? b. What shape will stay the same no matter how many degrees it is rotated? с.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.7: Polar Coordinates
Problem 110E
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**Exercise 3-37: Symmetry and Rotation** **Examine the figure graphed on the axes at right.** **a.** What happens when you rotate this figure about the origin by 90°, 45°, 180°? **b.** By what other angle could the figure at right be rotated so that the shape does not appear to change? **c.** What shape will stay the same no matter how many degrees it is rotated? **Graph Explanation:** The figure depicted is a symmetric star-like shape centered at the origin, which appears to have symmetry that could influence its appearance when rotated around the origin. It is placed on a set of x and y axes, with arrows indicating the positive directions. 1. **90° and 180° Rotations:** - Typically, a shape with bilateral or quadrilateral symmetry might not change visually at these angles. 2. **45° Rotation:** - A rotation by 45° might alter most figures unless they have particular rotational symmetry. 3. **Potential Symmetry Observations:** - The figure might not change in appearance at specific angles due to its symmetry. Understanding the rotational symmetry of geometric shapes helps in visualizing their transformations under different rotations.
Transcribed Image Text:**Exercise 3-37: Symmetry and Rotation** **Examine the figure graphed on the axes at right.** **a.** What happens when you rotate this figure about the origin by 90°, 45°, 180°? **b.** By what other angle could the figure at right be rotated so that the shape does not appear to change? **c.** What shape will stay the same no matter how many degrees it is rotated? **Graph Explanation:** The figure depicted is a symmetric star-like shape centered at the origin, which appears to have symmetry that could influence its appearance when rotated around the origin. It is placed on a set of x and y axes, with arrows indicating the positive directions. 1. **90° and 180° Rotations:** - Typically, a shape with bilateral or quadrilateral symmetry might not change visually at these angles. 2. **45° Rotation:** - A rotation by 45° might alter most figures unless they have particular rotational symmetry. 3. **Potential Symmetry Observations:** - The figure might not change in appearance at specific angles due to its symmetry. Understanding the rotational symmetry of geometric shapes helps in visualizing their transformations under different rotations.
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