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Which sequence of transformations takes AA to its image, AB ?

Which sequence of transformations takes AA to its image, AB ?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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### Transformations of Geometric Shapes **Question:** Which sequence of transformations takes triangle \( \Delta A \) to its image, \( \Delta B \)? **Choices:** A. Reflection over the \( x \)-axis and translation 2 units down B. Reflection over the \( y \)-axis and translation 2 units down C. Translation 2 units down and 90° rotation about the origin D. Translation 12 units right and 90° rotation about the origin **Diagram:** The diagram features a Cartesian coordinate plane with the \( x \)-axis and \( y \)-axis ranging from -10 to 10. Two triangles, \( \Delta A \) and \( \Delta B \), are shown on the graph. The triangle \( \Delta A \) is located in the second quadrant, and \( \Delta B \) is located in the first quadrant. **Analysis of Choices:** - **Choice A:** Reflection over the \( x \)-axis results in a triangle positioned below the \( x \)-axis. Translating it 2 units down moves it further into the negative \( y \)-region, which does not place it in the first quadrant like \( \Delta B \). - **Choice B:** Reflection over the \( y \)-axis results in a triangle positioned on the opposite side of the \( y \)-axis but remaining in the upper part of the coordinate plane. Translating it 2 units down does not place it in the correct position to match \( \Delta B \). - **Choice C:** Translation 2 units down moves the triangle 2 units lower within the same quadrant. A 90° rotation about the origin would not place it in the correct position as seen with \( \Delta B \)'s location. - **Choice D (Correct Answer):** Translating the triangle 12 units to the right moves \( \Delta A \) horizontally across the origin. A 90° rotation about the origin then positions the shape in the first quadrant correctly, aligning it to match \( \Delta B \). The correct transformation sequence to take \( \Delta A \) to its image \( \Delta B \) is therefore: **D. Translation 12 units right and 90° rotation about the origin.**
Transcribed Image Text:### Transformations of Geometric Shapes **Question:** Which sequence of transformations takes triangle \( \Delta A \) to its image, \( \Delta B \)? **Choices:** A. Reflection over the \( x \)-axis and translation 2 units down B. Reflection over the \( y \)-axis and translation 2 units down C. Translation 2 units down and 90° rotation about the origin D. Translation 12 units right and 90° rotation about the origin **Diagram:** The diagram features a Cartesian coordinate plane with the \( x \)-axis and \( y \)-axis ranging from -10 to 10. Two triangles, \( \Delta A \) and \( \Delta B \), are shown on the graph. The triangle \( \Delta A \) is located in the second quadrant, and \( \Delta B \) is located in the first quadrant. **Analysis of Choices:** - **Choice A:** Reflection over the \( x \)-axis results in a triangle positioned below the \( x \)-axis. Translating it 2 units down moves it further into the negative \( y \)-region, which does not place it in the first quadrant like \( \Delta B \). - **Choice B:** Reflection over the \( y \)-axis results in a triangle positioned on the opposite side of the \( y \)-axis but remaining in the upper part of the coordinate plane. Translating it 2 units down does not place it in the correct position to match \( \Delta B \). - **Choice C:** Translation 2 units down moves the triangle 2 units lower within the same quadrant. A 90° rotation about the origin would not place it in the correct position as seen with \( \Delta B \)'s location. - **Choice D (Correct Answer):** Translating the triangle 12 units to the right moves \( \Delta A \) horizontally across the origin. A 90° rotation about the origin then positions the shape in the first quadrant correctly, aligning it to match \( \Delta B \). The correct transformation sequence to take \( \Delta A \) to its image \( \Delta B \) is therefore: **D. Translation 12 units right and 90° rotation about the origin.**
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