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22. Describe a sequence of transformations that justify A DEF = ADE'F'. All rotations are centered at the origin. A. Two rotations 90° clockwise B. A rotation 90° clockwise and a reflection over the y-axis C. A rotation 90° counterclockwise and a reflection over the x-axis D. A rotation 90° clockwise and a translation left 10 units D' F' -6 -4 Q E 4 6 $

22. Describe a sequence of transformations that justify A DEF = ADE'F'. All rotations are centered at the origin. A. Two rotations 90° clockwise B. A rotation 90° clockwise and a reflection over the y-axis C. A rotation 90° counterclockwise and a reflection over the x-axis D. A rotation 90° clockwise and a translation left 10 units D' F' -6 -4 Q E 4 6 $

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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### Transformation and Congruence in Geometry #### Problem: **22. Describe a sequence of transformations that justify ΔDEF ≅ ΔD'E'F'. All rotations are centered at the origin.** #### Options: A. Two rotations 90° clockwise B. A rotation 90° clockwise and a reflection over the y-axis C. A rotation 90° counterclockwise and a reflection over the x-axis D. A rotation 90° clockwise and a translation left 10 units #### Explanation of the Graph: The graph depicts two triangles, ΔDEF and ΔD'E'F', on a coordinate plane. - Triangle ΔDEF has vertices located at: - D(4, 1) - E(4, 5) - F(7, 1) - Triangle ΔD'E'F' has vertices located at: - D'(-1, 4) - E'(-5, 4) - F'(-1, 7) A sequence of transformations involves changing a figure's position or orientation without altering its shape and size. The problem requires identifying the sequence of such transformations that can show that ΔDEF is congruent to ΔD'E'F'. #### Diagram Analysis: The diagram should help us visualize how one triangle can be transformed into another using rotations, reflections, or translations. 1. **Option A: Two rotations 90° clockwise** - First rotation: Moving ΔDEF 90° clockwise around the origin. - Second rotation: Moving the resulting position another 90° clockwise around the origin. 2. **Option B: A rotation 90° clockwise and a reflection over the y-axis** - A single 90° clockwise rotation might reorient the triangle, then reflecting it over the y-axis to possibly match the position of ΔD'E'F'. 3. **Option C**: A rotation 90° counterclockwise and a reflection over the x-axis - A single 90° counterclockwise rotation followed by a reflection over the x-axis could also position the triangle similarly. 4. **Option D: A rotation 90° clockwise and a translation left 10 units** - A single 90° clockwise rotation followed by shifting it left 10 units on the coordinate plane may place the triangle in a congruent position. The goal is to understand which transformation shows ΔDEF can be mapped precisely onto ΔD'E
Transcribed Image Text:### Transformation and Congruence in Geometry #### Problem: **22. Describe a sequence of transformations that justify ΔDEF ≅ ΔD'E'F'. All rotations are centered at the origin.** #### Options: A. Two rotations 90° clockwise B. A rotation 90° clockwise and a reflection over the y-axis C. A rotation 90° counterclockwise and a reflection over the x-axis D. A rotation 90° clockwise and a translation left 10 units #### Explanation of the Graph: The graph depicts two triangles, ΔDEF and ΔD'E'F', on a coordinate plane. - Triangle ΔDEF has vertices located at: - D(4, 1) - E(4, 5) - F(7, 1) - Triangle ΔD'E'F' has vertices located at: - D'(-1, 4) - E'(-5, 4) - F'(-1, 7) A sequence of transformations involves changing a figure's position or orientation without altering its shape and size. The problem requires identifying the sequence of such transformations that can show that ΔDEF is congruent to ΔD'E'F'. #### Diagram Analysis: The diagram should help us visualize how one triangle can be transformed into another using rotations, reflections, or translations. 1. **Option A: Two rotations 90° clockwise** - First rotation: Moving ΔDEF 90° clockwise around the origin. - Second rotation: Moving the resulting position another 90° clockwise around the origin. 2. **Option B: A rotation 90° clockwise and a reflection over the y-axis** - A single 90° clockwise rotation might reorient the triangle, then reflecting it over the y-axis to possibly match the position of ΔD'E'F'. 3. **Option C**: A rotation 90° counterclockwise and a reflection over the x-axis - A single 90° counterclockwise rotation followed by a reflection over the x-axis could also position the triangle similarly. 4. **Option D: A rotation 90° clockwise and a translation left 10 units** - A single 90° clockwise rotation followed by shifting it left 10 units on the coordinate plane may place the triangle in a congruent position. The goal is to understand which transformation shows ΔDEF can be mapped precisely onto ΔD'E
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