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Consider polygon ABCD, shown below. B E A G C IN D F

Consider polygon ABCD, shown below. B E A G C IN D F

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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### Analyzing Polygon ABCD #### Consider Polygon ABCD The image represents a polygon labeled ABCD on a coordinate grid. The vertices of the polygon are marked as points A, B, C, and D. 1. **Vertices Coordinates:** Each vertex is situated at specific coordinates on the grid: - **Vertex A:** Originating at the coordinate (0, 0) denoted as `A`. - **Vertex B:** Located at coordinate (0, 4) denoted as `B`. - **Vertex C:** At coordinate (4, 4) labeled as `C`. - **Vertex D:** Positioned at coordinate (4, 0) marked as `D`. 2. **Polygon Sides:** - **Side AB:** A vertical line segment from A to B. - **Side BC:** A horizontal line segment from B to C. - **Side CD:** A vertical line segment from C to D. - **Side DA:** A horizontal line segment from D to A. 3. **Diagonal BD:** - The diagonal line segment BD intersects the polygon from vertex B (0, 4) to vertex D (4, 0). - The intersection point of diagonal BD with the polygon is denoted as point G (2, 2). 4. **Coordinate Grid Details:** - The grid is marked by equidistant vertical and horizontal lines, forming 1x1 units. - Additional labels and points: - Point `E` is located along line segment AB, extending beyond B to (0, 5). - Point `F` is located along line segment CD, extending beyond D to (4, -1). This configuration clearly outlines the vertices and significant geometrical relationships within the polygon on the coordinate grid.
Transcribed Image Text:### Analyzing Polygon ABCD #### Consider Polygon ABCD The image represents a polygon labeled ABCD on a coordinate grid. The vertices of the polygon are marked as points A, B, C, and D. 1. **Vertices Coordinates:** Each vertex is situated at specific coordinates on the grid: - **Vertex A:** Originating at the coordinate (0, 0) denoted as `A`. - **Vertex B:** Located at coordinate (0, 4) denoted as `B`. - **Vertex C:** At coordinate (4, 4) labeled as `C`. - **Vertex D:** Positioned at coordinate (4, 0) marked as `D`. 2. **Polygon Sides:** - **Side AB:** A vertical line segment from A to B. - **Side BC:** A horizontal line segment from B to C. - **Side CD:** A vertical line segment from C to D. - **Side DA:** A horizontal line segment from D to A. 3. **Diagonal BD:** - The diagonal line segment BD intersects the polygon from vertex B (0, 4) to vertex D (4, 0). - The intersection point of diagonal BD with the polygon is denoted as point G (2, 2). 4. **Coordinate Grid Details:** - The grid is marked by equidistant vertical and horizontal lines, forming 1x1 units. - Additional labels and points: - Point `E` is located along line segment AB, extending beyond B to (0, 5). - Point `F` is located along line segment CD, extending beyond D to (4, -1). This configuration clearly outlines the vertices and significant geometrical relationships within the polygon on the coordinate grid.
### Transformations Teaching Tool **Question:** Select **all** the ways that describe rigid transformations that take AEFD to CFEB. **Options:** 1. □ Reflect AEFD across line EF. 2. □ Rotate AEFD 180 degrees counterclockwise around point G. 3. □ Rotate AEFD 180 degrees clockwise around point G. 4. □ Translate AEFD by the directed line segment from F to E, and then reflect across line FE. 5. □ Translate AEFD by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.
Transcribed Image Text:### Transformations Teaching Tool **Question:** Select **all** the ways that describe rigid transformations that take AEFD to CFEB. **Options:** 1. □ Reflect AEFD across line EF. 2. □ Rotate AEFD 180 degrees counterclockwise around point G. 3. □ Rotate AEFD 180 degrees clockwise around point G. 4. □ Translate AEFD by the directed line segment from F to E, and then reflect across line FE. 5. □ Translate AEFD by the directed line segment from F to E, and then rotate 180 degrees clockwise around point E.
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