**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.

The given figure is symmetric about the origin. Also when the figure rotates through any multiple of…

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**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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