The vertices of AABC are A(4,-1), B(-4,-4), and C(2,2). For the translation below, give the vertices of AA'B'C'. T(-36) (ДАВС) The vertices of AA'B'C' are A'B' and C (Simplify your answers. Type ordered pairs.)
The vertices of AABC are A(4,-1), B(-4,-4), and C(2,2). For the translation below, give the vertices of AA'B'C'. T(-36) (ДАВС) The vertices of AA'B'C' are A'B' and C (Simplify your answers. Type ordered pairs.)
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
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Question
![**Geometry Translation Problem**
In this exercise, we are given a triangle \( \triangle ABC \) with specific vertices and are asked to determine the vertices of the translated triangle \( \triangle A'B'C' \).
**Step-by-Step Solution:**
1. **Original Vertices:** The vertices of \( \triangle ABC \) are:
- \( A(4, -1) \)
- \( B(-4, -4) \)
- \( C(2, 2) \)
2. **Translation Vector:** The translation vector provided is \( T_{(-3,6)} \).
3. **Translation Process:** To find the new vertices of \( \triangle A'B'C' \), we apply the translation vector \( (-3, 6) \) to each vertex of \( \triangle ABC \):
- For vertex \( A \):
\[
A' = (4 - 3, -1 + 6) = (1, 5)
\]
- For vertex \( B \):
\[
B' = (-4 - 3, -4 + 6) = (-7, 2)
\]
- For vertex \( C \):
\[
C' = (2 - 3, 2 + 6) = (-1, 8)
\]
**Resulting Vertices:**
The vertices of \( \triangle A'B'C' \) are:
- \( A'(1, 5) \)
- \( B'(-7, 2) \)
- \( C'(-1, 8) \)
For an effective learning approach, it is essential to practice additional problems involving different translation vectors to understand the translation transformations comprehensively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfd810c3-21df-4807-835a-13eb9cacabea%2Fd53472fa-c0df-4fdb-89f9-6d7e7f0fbeb6%2Fh79l9ym_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Translation Problem**
In this exercise, we are given a triangle \( \triangle ABC \) with specific vertices and are asked to determine the vertices of the translated triangle \( \triangle A'B'C' \).
**Step-by-Step Solution:**
1. **Original Vertices:** The vertices of \( \triangle ABC \) are:
- \( A(4, -1) \)
- \( B(-4, -4) \)
- \( C(2, 2) \)
2. **Translation Vector:** The translation vector provided is \( T_{(-3,6)} \).
3. **Translation Process:** To find the new vertices of \( \triangle A'B'C' \), we apply the translation vector \( (-3, 6) \) to each vertex of \( \triangle ABC \):
- For vertex \( A \):
\[
A' = (4 - 3, -1 + 6) = (1, 5)
\]
- For vertex \( B \):
\[
B' = (-4 - 3, -4 + 6) = (-7, 2)
\]
- For vertex \( C \):
\[
C' = (2 - 3, 2 + 6) = (-1, 8)
\]
**Resulting Vertices:**
The vertices of \( \triangle A'B'C' \) are:
- \( A'(1, 5) \)
- \( B'(-7, 2) \)
- \( C'(-1, 8) \)
For an effective learning approach, it is essential to practice additional problems involving different translation vectors to understand the translation transformations comprehensively.
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