Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Translation/Rotation Quiz: Educational Content
#### Question:
**Suppose △DEF is the image of a translation of △ABC. If D is at (-6, -2), what translation rule maps △ABC to △DEF?**
#### Graph Interpretation:
In the provided graph, triangles △ABC and △DEF are illustrated on a coordinate plane. The coordinates for triangle △ABC are as follows:
- \( A (1, 1) \)
- \( B (3, -1) \)
- \( C (2, -2) \)
The point \( D \) of triangle △DEF is given at coordinates (-6, -2). The task is to determine the translation rule (T) that maps △ABC to △DEF.
#### Answer Options:
A. \( T_{0, -2}\)(△ABC) = △DEF
B. \( T_{6, -2}\)(△ABC) = △DEF
C. \( T_{-9, 2}\)(△ABC) = △DEF
D. \( T_{-9, -3}\)(△ABC) = △DEF
**Steps for Finding the Correct Translation Rule:**
1. Calculate the vector from point \( A \) of △ABC to point \( D \) of △DEF.
- Starting from \( A(1, 1) \) to \( D(-6, -2) \)
- Translation vector: \( D - A = (-6 - 1, -2 - 1) = (-7, -3) \)
2. Apply the same translation vector to points \( B \) and \( C \) of △ABC:
- For point \( B(3, -1) \):
- New coordinates: \( (3 - 7, -1 - 3) = (-4, -4) \)
- For point \( C(2, -2) \):
- New coordinates: \( (2 - 7, -2 - 3) = (-5, -5) \)
3. Verify if these new coordinates correspond to points E and F of △DEF as per the given graph.
Based on the given answer choices, the closest match to the correct translation rule is:
\[ T_{-7, -3}\]
However, reviewing the given options, there might be a typographical error. The correct answer may not be explicitly listed among the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfd810c3-21df-4807-835a-13eb9cacabea%2Ff4d95fda-242c-4ee9-879e-8313a8614fc4%2Fsenq07f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Translation/Rotation Quiz: Educational Content
#### Question:
**Suppose △DEF is the image of a translation of △ABC. If D is at (-6, -2), what translation rule maps △ABC to △DEF?**
#### Graph Interpretation:
In the provided graph, triangles △ABC and △DEF are illustrated on a coordinate plane. The coordinates for triangle △ABC are as follows:
- \( A (1, 1) \)
- \( B (3, -1) \)
- \( C (2, -2) \)
The point \( D \) of triangle △DEF is given at coordinates (-6, -2). The task is to determine the translation rule (T) that maps △ABC to △DEF.
#### Answer Options:
A. \( T_{0, -2}\)(△ABC) = △DEF
B. \( T_{6, -2}\)(△ABC) = △DEF
C. \( T_{-9, 2}\)(△ABC) = △DEF
D. \( T_{-9, -3}\)(△ABC) = △DEF
**Steps for Finding the Correct Translation Rule:**
1. Calculate the vector from point \( A \) of △ABC to point \( D \) of △DEF.
- Starting from \( A(1, 1) \) to \( D(-6, -2) \)
- Translation vector: \( D - A = (-6 - 1, -2 - 1) = (-7, -3) \)
2. Apply the same translation vector to points \( B \) and \( C \) of △ABC:
- For point \( B(3, -1) \):
- New coordinates: \( (3 - 7, -1 - 3) = (-4, -4) \)
- For point \( C(2, -2) \):
- New coordinates: \( (2 - 7, -2 - 3) = (-5, -5) \)
3. Verify if these new coordinates correspond to points E and F of △DEF as per the given graph.
Based on the given answer choices, the closest match to the correct translation rule is:
\[ T_{-7, -3}\]
However, reviewing the given options, there might be a typographical error. The correct answer may not be explicitly listed among the
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