10 6. M -10 -8 -6 -4 2 4 6 8 0 A -6 -8 -10 Describe how circle A is transformed into circle M. Translate circle A: (x, y) → (x+ > Y+ Dilate the translated image about its new center by scale factor 4.
10 6. M -10 -8 -6 -4 2 4 6 8 0 A -6 -8 -10 Describe how circle A is transformed into circle M. Translate circle A: (x, y) → (x+ > Y+ Dilate the translated image about its new center by scale factor 4.
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Transformation of Circle A to Circle M
The diagram shows two circles, Circle A and Circle M, on a coordinate plane. Circle A is located in the second quadrant with its center at the coordinates (-5, -5) and Circle M is located in the first quadrant with its center at the coordinates (4, 3).
To describe the transformation of Circle A into Circle M, follow these steps:
1. **Translation**:
- Translate Circle A from its current center at \( (x, y) \) to a new position. Use the transformation function:
\[
(x, y) \rightarrow (x + \_\_\_, y + \_\_\_)
\]
- Horizontal Translation: Move the center of Circle A from \(-5\) to \(4\), a shift of \(4 - (-5) = 9\) units to the right.
- Vertical Translation: Move the center of Circle A from \(-5\) to \(3\), a shift of \(3 - (-5) = 8\) units up.
2. **Dilation**:
- Dilate the translated image about its new center by scale factor \( \_ \)
- Using the grid, we can determine the radius of Circle A to be approximately 3 units and the radius of Circle M to be approximately 7 units.
- The scale factor is the ratio of the radii: \( \frac{7}{3} \).
**Final Transformation Steps**:
- Translate Circle A by:
\[
(x, y) \rightarrow (x + 9, y + 8)
\]
- Dilate about the new center by a scale factor of:
\[
\frac{7}{3}
\]
### Detailed Breakdown of Graph Elements:
- **Coordinate Plane**:
- The coordinate grid has both the x-axis and the y-axis, delineating positive and negative quadrants.
- The x-axis ranges from -10 to 10, and the y-axis also ranges from -10 to 10.
- **Circles and Centers**:
- **Circle A**: Located in the second quadrant with its center at (-5, -5).
- **Circle M**: Located in the first quadrant with its center at (4, 3).
By following these steps, one can effectively transform Circle A into](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedcbec6a-306c-41d4-8bd4-863550c43245%2F27171710-90ae-4060-96e7-df92348b02a5%2Fs79d4h5_processed.png&w=3840&q=75)
Transcribed Image Text:### Transformation of Circle A to Circle M
The diagram shows two circles, Circle A and Circle M, on a coordinate plane. Circle A is located in the second quadrant with its center at the coordinates (-5, -5) and Circle M is located in the first quadrant with its center at the coordinates (4, 3).
To describe the transformation of Circle A into Circle M, follow these steps:
1. **Translation**:
- Translate Circle A from its current center at \( (x, y) \) to a new position. Use the transformation function:
\[
(x, y) \rightarrow (x + \_\_\_, y + \_\_\_)
\]
- Horizontal Translation: Move the center of Circle A from \(-5\) to \(4\), a shift of \(4 - (-5) = 9\) units to the right.
- Vertical Translation: Move the center of Circle A from \(-5\) to \(3\), a shift of \(3 - (-5) = 8\) units up.
2. **Dilation**:
- Dilate the translated image about its new center by scale factor \( \_ \)
- Using the grid, we can determine the radius of Circle A to be approximately 3 units and the radius of Circle M to be approximately 7 units.
- The scale factor is the ratio of the radii: \( \frac{7}{3} \).
**Final Transformation Steps**:
- Translate Circle A by:
\[
(x, y) \rightarrow (x + 9, y + 8)
\]
- Dilate about the new center by a scale factor of:
\[
\frac{7}{3}
\]
### Detailed Breakdown of Graph Elements:
- **Coordinate Plane**:
- The coordinate grid has both the x-axis and the y-axis, delineating positive and negative quadrants.
- The x-axis ranges from -10 to 10, and the y-axis also ranges from -10 to 10.
- **Circles and Centers**:
- **Circle A**: Located in the second quadrant with its center at (-5, -5).
- **Circle M**: Located in the first quadrant with its center at (4, 3).
By following these steps, one can effectively transform Circle A into
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