**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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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

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

**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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