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What is the degree of rotation that takes quadrilateral FGHI to F'G'H'I'? G.

What is the degree of rotation that takes quadrilateral FGHI to F'G'H'I'? G.

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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### What makes a polygon a regular polygon? --- A polygon is defined as a two-dimensional geometric figure with straight sides. When categorizing polygons, one important classification is whether they are regular or irregular. A **regular polygon** is a polygon with all sides of equal length and all interior angles of equal measure. Examples of regular polygons include equilateral triangles, squares, and regular hexagons. In contrast, an **irregular polygon** has sides of different lengths and angles of different measures. Understanding the properties of regular polygons is critical in various fields, including geometry, architecture, and computer graphics. #### Key Characteristics of Regular Polygons: - **Equal Side Lengths:** Every side has the same length. - **Equal Angles:** All interior angles are equal. - **Symmetry:** Regular polygons are symmetrical about their center. Understanding and distinguishing between regular and irregular polygons is fundamental in the study of geometry and helps in various applications and problem-solving scenarios.
Transcribed Image Text:### What makes a polygon a regular polygon? --- A polygon is defined as a two-dimensional geometric figure with straight sides. When categorizing polygons, one important classification is whether they are regular or irregular. A **regular polygon** is a polygon with all sides of equal length and all interior angles of equal measure. Examples of regular polygons include equilateral triangles, squares, and regular hexagons. In contrast, an **irregular polygon** has sides of different lengths and angles of different measures. Understanding the properties of regular polygons is critical in various fields, including geometry, architecture, and computer graphics. #### Key Characteristics of Regular Polygons: - **Equal Side Lengths:** Every side has the same length. - **Equal Angles:** All interior angles are equal. - **Symmetry:** Regular polygons are symmetrical about their center. Understanding and distinguishing between regular and irregular polygons is fundamental in the study of geometry and helps in various applications and problem-solving scenarios.
**Rotation of Quadrilaterals** **Question:** What is the degree of rotation that takes quadrilateral FGHI to F'G'H'I'? **Analysis:** The diagram provided consists of two quadrilaterals, FGHI and its rotated image F'G'H'I', plotted on a coordinate grid. - **Quadrilateral FGHI** is plotted within the first quadrant such that: - Point F lies at (2,2), - Point G lies at (2,4), - Point H lies at (4,5), - Point I lies at (4,3). This quadrilateral is shown in black. - **Quadrilateral F'G'H'I'** appears in a rotated position with: - Point F' at (-2,-2), - Point G' at (-4,-2), - Point H' at (-5,-4), - Point I' at (-3,-4). This image is shown in blue. Given these coordinates and their symmetry about the origin, the rotation appears to be a 180-degree rotation about the origin. **Conclusion:** The degree of rotation that takes quadrilateral FGHI to its image F'G'H'I' is 180 degrees.
Transcribed Image Text:**Rotation of Quadrilaterals** **Question:** What is the degree of rotation that takes quadrilateral FGHI to F'G'H'I'? **Analysis:** The diagram provided consists of two quadrilaterals, FGHI and its rotated image F'G'H'I', plotted on a coordinate grid. - **Quadrilateral FGHI** is plotted within the first quadrant such that: - Point F lies at (2,2), - Point G lies at (2,4), - Point H lies at (4,5), - Point I lies at (4,3). This quadrilateral is shown in black. - **Quadrilateral F'G'H'I'** appears in a rotated position with: - Point F' at (-2,-2), - Point G' at (-4,-2), - Point H' at (-5,-4), - Point I' at (-3,-4). This image is shown in blue. Given these coordinates and their symmetry about the origin, the rotation appears to be a 180-degree rotation about the origin. **Conclusion:** The degree of rotation that takes quadrilateral FGHI to its image F'G'H'I' is 180 degrees.
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