1. After applying a dilation centered at O, the figure below becomes 17 cm wide and H cm tall. 1 cm OF 1 cm Original a. What is the new spacing between the grid lines? Explain! b. How tall does the figure become? Use our definition of multiplication (and division) to write different equations that relate H to other quantities. Interpret the parts of your equations in terms of the figure and the grid lines. 2. After applying a dilation centered at O, the figure above becomes X cm wide and Y cm tall. a. What is the new spacing between the grid lines? Explain! b. How are X and Y related? Use our definition of multiplication (and division) to write different equations relating X and Y. Interpret the parts of your equations in terms of the figure and the grid lines.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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i need help with 2. a and b please!!!!
**Educational Website Text Transcription**

---

**1. Geometric Dilations: Understanding Changes in Dimensions**

The figure shown below undergoes a dilation centered at point O. After the dilation, the figure becomes 17 cm wide and \( H \) cm tall.

![Original Figure]

The original figure has the following dimensions:
- Each grid line is spaced 1 cm apart. 

*Questions:*

a. **What is the new spacing between the grid lines? Explain!**

b. **How tall does the figure become?** Use our definition of multiplication (and division) to write different equations that relate \( H \) to other quantities. Interpret the parts of your equations in terms of the figure and the grid lines.

---

**2. General Case of Geometric Dilations**

Under a similar dilation centered at point O, a generic figure becomes \( X \) cm wide and \( Y \) cm tall.

*Questions:*

a. **What is the new spacing between the grid lines? Explain!**

b. **How are \( X \) and \( Y \) related?** Use our definition of multiplication (and division) to write different equations relating \( X \) and \( Y \). Interpret the parts of your equations in terms of the figure and the grid lines.

---

**Explanation of Diagram:**

The diagram of the original figure consists of a grid where each cell is 1 cm by 1 cm. The grid lines are placed 1 cm apart, both horizontally and vertically. The central point O is located at the bottom left corner of the figure, acting as the center of dilation. 

When the figure is dilated, its new dimensions and grid line spacing depend on the dilation factor. Understanding this change is key to solving the questions provided.

---

This exercise aims to deepen your understanding of how dilations affect spatial properties and mathematical relationships between dimensions.

---

*End of Transcription*

For any additional questions or clarifications, please refer to the provided diagram and mathematical definitions of dilation.
Transcribed Image Text:**Educational Website Text Transcription** --- **1. Geometric Dilations: Understanding Changes in Dimensions** The figure shown below undergoes a dilation centered at point O. After the dilation, the figure becomes 17 cm wide and \( H \) cm tall. ![Original Figure] The original figure has the following dimensions: - Each grid line is spaced 1 cm apart. *Questions:* a. **What is the new spacing between the grid lines? Explain!** b. **How tall does the figure become?** Use our definition of multiplication (and division) to write different equations that relate \( H \) to other quantities. Interpret the parts of your equations in terms of the figure and the grid lines. --- **2. General Case of Geometric Dilations** Under a similar dilation centered at point O, a generic figure becomes \( X \) cm wide and \( Y \) cm tall. *Questions:* a. **What is the new spacing between the grid lines? Explain!** b. **How are \( X \) and \( Y \) related?** Use our definition of multiplication (and division) to write different equations relating \( X \) and \( Y \). Interpret the parts of your equations in terms of the figure and the grid lines. --- **Explanation of Diagram:** The diagram of the original figure consists of a grid where each cell is 1 cm by 1 cm. The grid lines are placed 1 cm apart, both horizontally and vertically. The central point O is located at the bottom left corner of the figure, acting as the center of dilation. When the figure is dilated, its new dimensions and grid line spacing depend on the dilation factor. Understanding this change is key to solving the questions provided. --- This exercise aims to deepen your understanding of how dilations affect spatial properties and mathematical relationships between dimensions. --- *End of Transcription* For any additional questions or clarifications, please refer to the provided diagram and mathematical definitions of dilation.
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