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.4 3 -2 L.CGL D. 3 45 5-4-3-2 -1 -2 -4

.4 3 -2 L.CGL D. 3 45 5-4-3-2 -1 -2 -4

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 is the equation of the larger circle?
Here's a transcription of the image along with a detailed explanation of the graphs for an educational website: --- **Coordinate Geometry and Circles** In this diagram, we see two circles positioned on a coordinate plane with both x and y axes clearly marked in conjunction with coordinate points. 1. **Larger Circle**: - The larger circle has its center at point P, which appears to be located at approximately (-2, 1). - The circle's radius extends from the center, reaching to the points on the circle. One can estimate the radius by counting the units from the center to any point on the perimeter, which looks to be approximately 3 units. 2. **Smaller Circle**: - The smaller circle has its center at point Z, located at the coordinates (2, -3). - Similarly, the radius of this smaller circle is approximately 2 units, inferred by counting the units from the center to the perimeter. **Axes and Points**: - The x-axis is labeled with points A and B for reference. - Point A is positioned at (-5, 0). - Point B is positioned at (5, 0). - The y-axis shows point C for additional reference. - Point C is found at (0, 5). **Graph Interpretation**: - The thick grid lines in the background aid in locating and plotting points accurately by providing a visual framework. - The standard positive direction for both axes is indicated by arrows, facilitating understanding of the orientation. These circles and the coordinate system setup provide an excellent way to understand geometric properties and the use of coordinate planes in graphing shapes. By marking points and measuring distances using the grid, one can derive various mathematical relationships and properties essential in geometry. --- This description would assist in educational contexts where understanding and interpreting graphs, coordinates, and geometric shapes are crucial.
Transcribed Image Text:Here's a transcription of the image along with a detailed explanation of the graphs for an educational website: --- **Coordinate Geometry and Circles** In this diagram, we see two circles positioned on a coordinate plane with both x and y axes clearly marked in conjunction with coordinate points. 1. **Larger Circle**: - The larger circle has its center at point P, which appears to be located at approximately (-2, 1). - The circle's radius extends from the center, reaching to the points on the circle. One can estimate the radius by counting the units from the center to any point on the perimeter, which looks to be approximately 3 units. 2. **Smaller Circle**: - The smaller circle has its center at point Z, located at the coordinates (2, -3). - Similarly, the radius of this smaller circle is approximately 2 units, inferred by counting the units from the center to the perimeter. **Axes and Points**: - The x-axis is labeled with points A and B for reference. - Point A is positioned at (-5, 0). - Point B is positioned at (5, 0). - The y-axis shows point C for additional reference. - Point C is found at (0, 5). **Graph Interpretation**: - The thick grid lines in the background aid in locating and plotting points accurately by providing a visual framework. - The standard positive direction for both axes is indicated by arrows, facilitating understanding of the orientation. These circles and the coordinate system setup provide an excellent way to understand geometric properties and the use of coordinate planes in graphing shapes. By marking points and measuring distances using the grid, one can derive various mathematical relationships and properties essential in geometry. --- This description would assist in educational contexts where understanding and interpreting graphs, coordinates, and geometric shapes are crucial.
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