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Draw the image of AABC under a translation by 5 units to the left. 7- 4+ -7 -6 -5 -4 -32 1 23 4 5 6 7 -3+ -4 -5+ -6- 6. 3.

Draw the image of AABC under a translation by 5 units to the left. 7- 4+ -7 -6 -5 -4 -32 1 23 4 5 6 7 -3+ -4 -5+ -6- 6. 3.

Elementary Geometry For College Students, 7e
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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**Title: Understanding Translation of Triangles on a Coordinate Plane** **Topic: Translating Geometric Figures** --- **Objective:** Learn how to translate the image of a triangle on a coordinate plane. **Instructions:** The given task is to draw the image of triangle \( \triangle ABC \) under a translation by 5 units to the left. **Graphical Explanation:** 1. **Triangle \( \triangle ABC \):** - The triangle is plotted on a coordinate plane. - Vertices of the triangle: - Point \( A \) is located at (2, 2). - Point \( B \) is at (2, -3). - Point \( C \) is at (3, -1). - The vertices are connected forming \( \triangle ABC \). 2. **Translation by 5 Units to the Left:** - Translation means moving every point of the shape a certain number of units in a specified direction. - In this case, we move each vertex of \( \triangle ABC \) 5 units to the left. 3. **New Coordinates after Translation:** - Point \( A \) moves from (2, 2) to (2 - 5, 2) = (-3, 2). - Point \( B \) moves from (2, -3) to (2 - 5, -3) = (-3, -3). - Point \( C \) moves from (3, -1) to (3 - 5, -1) = (-2, -1). 4. **Transformed Triangle \( \triangle A'B'C' \):** - The new vertices after translation are: - Point \( A' \) at (-3, 2). - Point \( B' \) at (-3, -3). - Point \( C' \) at (-2, -1). - The vertices are connected forming \( \triangle A'B'C' \). **Visual Representation:** - The coordinate plane in the visual shows both the original \( \triangle ABC \) (in green) and the translated \( \triangle A'B'C' \) (in blue). - \( \triangle A'B'C' \) is accurately 5 units to the left of \( \triangle ABC \). --- This process helps understand the impact of translating figures on a coordinate plane
Transcribed Image Text:**Title: Understanding Translation of Triangles on a Coordinate Plane** **Topic: Translating Geometric Figures** --- **Objective:** Learn how to translate the image of a triangle on a coordinate plane. **Instructions:** The given task is to draw the image of triangle \( \triangle ABC \) under a translation by 5 units to the left. **Graphical Explanation:** 1. **Triangle \( \triangle ABC \):** - The triangle is plotted on a coordinate plane. - Vertices of the triangle: - Point \( A \) is located at (2, 2). - Point \( B \) is at (2, -3). - Point \( C \) is at (3, -1). - The vertices are connected forming \( \triangle ABC \). 2. **Translation by 5 Units to the Left:** - Translation means moving every point of the shape a certain number of units in a specified direction. - In this case, we move each vertex of \( \triangle ABC \) 5 units to the left. 3. **New Coordinates after Translation:** - Point \( A \) moves from (2, 2) to (2 - 5, 2) = (-3, 2). - Point \( B \) moves from (2, -3) to (2 - 5, -3) = (-3, -3). - Point \( C \) moves from (3, -1) to (3 - 5, -1) = (-2, -1). 4. **Transformed Triangle \( \triangle A'B'C' \):** - The new vertices after translation are: - Point \( A' \) at (-3, 2). - Point \( B' \) at (-3, -3). - Point \( C' \) at (-2, -1). - The vertices are connected forming \( \triangle A'B'C' \). **Visual Representation:** - The coordinate plane in the visual shows both the original \( \triangle ABC \) (in green) and the translated \( \triangle A'B'C' \) (in blue). - \( \triangle A'B'C' \) is accurately 5 units to the left of \( \triangle ABC \). --- This process helps understand the impact of translating figures on a coordinate plane
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