Becca performed two transformations on triangle ABC to create triangle A"B"C", but she can't remember the order she performed them. She either rotated the triangle 90* clockwise about the origin and then dilated it by a scale factor of with a center of dilation at the origin, or she performed the transformations in the opposite order. N PÅ B" Which order did Becca perform the transformations? Choose one option from each drop-down menu to answer the question. Becca Choose. resulting triangle would be Choose.. ✓ If she rotated triangle ABC and then dilated it, the ✓on the coordinate grid. If she dilated triangle ABC and then rotated it, the resulting triangle would be Choose. grid. ✓on the coordinate
Becca performed two transformations on triangle ABC to create triangle A"B"C", but she can't remember the order she performed them. She either rotated the triangle 90* clockwise about the origin and then dilated it by a scale factor of with a center of dilation at the origin, or she performed the transformations in the opposite order. N PÅ B" Which order did Becca perform the transformations? Choose one option from each drop-down menu to answer the question. Becca Choose. resulting triangle would be Choose.. ✓ If she rotated triangle ABC and then dilated it, the ✓on the coordinate grid. If she dilated triangle ABC and then rotated it, the resulting triangle would be Choose. grid. ✓on the coordinate
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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![**Educational Content: Transcription and Explanation**
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**Text Transcription:**
Becca performed two transformations on triangle \(ABC\) to create triangle \(A''B''C''\), but she can’t remember the order she performed them. She either rotated the triangle \(90^\circ\) clockwise about the origin and then dilated it by a scale factor of \(\frac{1}{2}\) with a center of dilation at the origin, or she performed the transformations in the opposite order.
**Question:**
Which order did Becca perform the transformations? Choose one option from each drop-down menu to answer the question.
Becca [Choose…] If she rotated triangle \(ABC\) and then dilated it, the resulting triangle would be [Choose…] on the coordinate grid. If she dilated triangle \(ABC\) and then rotated it, the resulting triangle would be [Choose…] on the coordinate grid.
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**Graphs/Diagrams Explanation:**
The graph on the left side shows two triangles on a coordinate grid:
1. **Triangle \(ABC\)**:
- Placed in the first quadrant.
- \(A\) is located at \( (0, 2) \).
- \(B\) is located at \( (3, 1) \).
- \(C\) is located at \( (5, 6) \).
2. **Triangle \(A''B''C''\)**:
- Placed in the second quadrant.
- \(A''\) is located at \( (-1, 0) \).
- \(B''\) is located at \( (-0.5, -1.5) \).
- \(C''\) is located at \( (-3, -2.5) \).
The coordinate grid has the x-axis and y-axis marked with values from \(-6\) to \(6\).
**Analysis:**
- **Rotation**: A \(90^\circ\) clockwise rotation would position points differently than a dilation.
- **Dilation**: With a scale factor of \(\frac{1}{2}\), all points would move closer to the origin, halving their distances from it.
Understanding these transformations will help determine the sequence Becca used based on the resulting changes in position and size.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ccaa343-d51e-49ad-b600-181f88993167%2F1a4aad61-c90d-4fec-8a56-97e7a0586777%2F9x46j0s_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Transcription and Explanation**
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**Text Transcription:**
Becca performed two transformations on triangle \(ABC\) to create triangle \(A''B''C''\), but she can’t remember the order she performed them. She either rotated the triangle \(90^\circ\) clockwise about the origin and then dilated it by a scale factor of \(\frac{1}{2}\) with a center of dilation at the origin, or she performed the transformations in the opposite order.
**Question:**
Which order did Becca perform the transformations? Choose one option from each drop-down menu to answer the question.
Becca [Choose…] If she rotated triangle \(ABC\) and then dilated it, the resulting triangle would be [Choose…] on the coordinate grid. If she dilated triangle \(ABC\) and then rotated it, the resulting triangle would be [Choose…] on the coordinate grid.
---
**Graphs/Diagrams Explanation:**
The graph on the left side shows two triangles on a coordinate grid:
1. **Triangle \(ABC\)**:
- Placed in the first quadrant.
- \(A\) is located at \( (0, 2) \).
- \(B\) is located at \( (3, 1) \).
- \(C\) is located at \( (5, 6) \).
2. **Triangle \(A''B''C''\)**:
- Placed in the second quadrant.
- \(A''\) is located at \( (-1, 0) \).
- \(B''\) is located at \( (-0.5, -1.5) \).
- \(C''\) is located at \( (-3, -2.5) \).
The coordinate grid has the x-axis and y-axis marked with values from \(-6\) to \(6\).
**Analysis:**
- **Rotation**: A \(90^\circ\) clockwise rotation would position points differently than a dilation.
- **Dilation**: With a scale factor of \(\frac{1}{2}\), all points would move closer to the origin, halving their distances from it.
Understanding these transformations will help determine the sequence Becca used based on the resulting changes in position and size.
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