The vertices of a rectangle are R(-5,-5), S(-1, -5), T(-1, 1) and U(-5, 1). After translation, R' is the point (3, 0). Find the translation and coordinates of U'.
The vertices of a rectangle are R(-5,-5), S(-1, -5), T(-1, 1) and U(-5, 1). After translation, R' is the point (3, 0). Find the translation and coordinates of U'.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.CT: Chapter Test
Problem 8CT
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![### Problem 2
The vertices of a rectangle are \(R(-5, -5)\), \(S(-1, -5)\), \(T(-1, 1)\), and \(U(-5, 1)\). After a translation, \(R'\) is the point \( (3, 0) \). Find the translation and coordinates of \(U'\).
[A] \(⟨8, -5⟩; (3, -4)\)
[B] \(⟨5, -8⟩; (0, -7)\)
[C] \(⟨-5, 8⟩; (-10, 9)\)
[D] \(⟨8, 5⟩; (3, 6)\)
**Answer:** _______________
---
**Explanation:**
1. Identify the coordinates of \(R\) before the translation: \( (-5, -5) \).
2. Identify the coordinates of \(R'\) after the translation: \( (3, 0) \).
3. Calculate the translation vector by finding the difference between the coordinates of \(R'\) and \(R\):
\[
\text{Translation vector} = (3 - (-5), 0 - (-5)) = (8, 5)
\]
4. Apply the translation vector to point \(U(-5, 1)\) to get \(U'\):
\[
U' = (-5 + 8, 1 + 5) = (3, 6)
\]
5. Confirm that the answer is option [D]:
\[
[D] \quad ⟨8, 5⟩; (3, 6)
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Transcribed Image Text:### Problem 2
The vertices of a rectangle are \(R(-5, -5)\), \(S(-1, -5)\), \(T(-1, 1)\), and \(U(-5, 1)\). After a translation, \(R'\) is the point \( (3, 0) \). Find the translation and coordinates of \(U'\).
[A] \(⟨8, -5⟩; (3, -4)\)
[B] \(⟨5, -8⟩; (0, -7)\)
[C] \(⟨-5, 8⟩; (-10, 9)\)
[D] \(⟨8, 5⟩; (3, 6)\)
**Answer:** _______________
---
**Explanation:**
1. Identify the coordinates of \(R\) before the translation: \( (-5, -5) \).
2. Identify the coordinates of \(R'\) after the translation: \( (3, 0) \).
3. Calculate the translation vector by finding the difference between the coordinates of \(R'\) and \(R\):
\[
\text{Translation vector} = (3 - (-5), 0 - (-5)) = (8, 5)
\]
4. Apply the translation vector to point \(U(-5, 1)\) to get \(U'\):
\[
U' = (-5 + 8, 1 + 5) = (3, 6)
\]
5. Confirm that the answer is option [D]:
\[
[D] \quad ⟨8, 5⟩; (3, 6)
\]
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