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.4 -2 GLCGL D 1 5-4-3 -2 3. -4 B -5 2. 寸の

.4 -2 GLCGL D 1 5-4-3 -2 3. -4 B -5 2. 寸の

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 smaller circle ?
The image is a graph with two circles plotted within a Cartesian coordinate system. Below is a detailed transcription and explanation suitable for an educational website: **Graph Description:** **Coordinate System:** The graph is a Cartesian coordinate system with the x-axis and y-axis intersecting at the origin (0,0). The axes extend from -5 to 5 on both the x and y axes. Each unit on both axes is represented by a line, creating a grid of squares with each side equal to one unit. **Circles:** 1. **Larger Circle:** - **Center:** The center of the large circle is at the coordinates (-2, 1). - **Radius:** The radius of the large circle extends from its center to any point on its circumference. For example, one point on the circumference passes through approximately (-5, 1). - **Point P:** There is a point labeled P located at (-2, 1), the center of the larger circle. 2. **Smaller Circle:** - **Center:** The center of the smaller circle is at the coordinates (3, -3). - **Radius:** The radius of the smaller circle extends from its center to any point on its circumference. For example, one point on the circumference passes through approximately (3, -5). - **Point Z:** There is a point labeled Z located at (3, -3), the center of the smaller circle. **Labeled Points on the Axes:** - Point A is located at (-5, 0) on the x-axis. - Point B is located at (5, 0) on the x-axis. - Point C is located at (0, 5) on the y-axis. **Observations:** - Point P is notably marked and lies at the center of the larger circle. - Point Z is similarly marked and lies at the center of the smaller circle. - The smaller circle is positioned such that its diameter is parallel and directly below the x-axis. This graph effectively demonstrates the properties of circles in a coordinate system, including their centers, radii, and how to graphically represent points on a plane.
Transcribed Image Text:The image is a graph with two circles plotted within a Cartesian coordinate system. Below is a detailed transcription and explanation suitable for an educational website: **Graph Description:** **Coordinate System:** The graph is a Cartesian coordinate system with the x-axis and y-axis intersecting at the origin (0,0). The axes extend from -5 to 5 on both the x and y axes. Each unit on both axes is represented by a line, creating a grid of squares with each side equal to one unit. **Circles:** 1. **Larger Circle:** - **Center:** The center of the large circle is at the coordinates (-2, 1). - **Radius:** The radius of the large circle extends from its center to any point on its circumference. For example, one point on the circumference passes through approximately (-5, 1). - **Point P:** There is a point labeled P located at (-2, 1), the center of the larger circle. 2. **Smaller Circle:** - **Center:** The center of the smaller circle is at the coordinates (3, -3). - **Radius:** The radius of the smaller circle extends from its center to any point on its circumference. For example, one point on the circumference passes through approximately (3, -5). - **Point Z:** There is a point labeled Z located at (3, -3), the center of the smaller circle. **Labeled Points on the Axes:** - Point A is located at (-5, 0) on the x-axis. - Point B is located at (5, 0) on the x-axis. - Point C is located at (0, 5) on the y-axis. **Observations:** - Point P is notably marked and lies at the center of the larger circle. - Point Z is similarly marked and lies at the center of the smaller circle. - The smaller circle is positioned such that its diameter is parallel and directly below the x-axis. This graph effectively demonstrates the properties of circles in a coordinate system, including their centers, radii, and how to graphically represent points on a plane.
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