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The center of an earthquake, called an epicenter, has occurred in a city located at the coordinates (1,-4). Earthquakes can be felt in every direction from its epicenter, equal distances away in every direction. This specific earthquake was felt as far away as a city located at (-3,2).

The center of an earthquake, called an epicenter, has occurred in a city located at the coordinates (1,-4). Earthquakes can be felt in every direction from its epicenter, equal distances away in every direction. This specific earthquake was felt as far away as a city located at (-3,2).

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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### Understanding Earthquake Epicenters and Their Reach The center of an earthquake, called an epicenter, has occurred in a city located at the coordinates (1, -4). Earthquakes can be felt in every direction from their epicenter, extending outwards equally in all directions. This specific earthquake was felt as far away as a city located at (-3, 2). ### Graph Explanation The accompanying diagram is a coordinate plane depicting the earthquake's epicenter and the furthest point at which the earthquake was felt. - The graph is a standard Cartesian grid with the x-axis (horizontal) and y-axis (vertical). - The x-axis and y-axis both range from -8 to 8, providing a broad view of the area. - The epicenter is marked at the coordinates (1, -4), which lies one unit to the right of the origin (0, 0) and four units down. - The point where the earthquake was also felt is marked at (-3, 2), which is three units to the left of the origin and two units up. The grid includes multiple colored markers and tools on the left side, likely for annotative and interactive purposes. --- This visualization helps in understanding how the seismic waves spread from the epicenter to distant locales, reaching places as far as (-3, 2).
Transcribed Image Text:### Understanding Earthquake Epicenters and Their Reach The center of an earthquake, called an epicenter, has occurred in a city located at the coordinates (1, -4). Earthquakes can be felt in every direction from their epicenter, extending outwards equally in all directions. This specific earthquake was felt as far away as a city located at (-3, 2). ### Graph Explanation The accompanying diagram is a coordinate plane depicting the earthquake's epicenter and the furthest point at which the earthquake was felt. - The graph is a standard Cartesian grid with the x-axis (horizontal) and y-axis (vertical). - The x-axis and y-axis both range from -8 to 8, providing a broad view of the area. - The epicenter is marked at the coordinates (1, -4), which lies one unit to the right of the origin (0, 0) and four units down. - The point where the earthquake was also felt is marked at (-3, 2), which is three units to the left of the origin and two units up. The grid includes multiple colored markers and tools on the left side, likely for annotative and interactive purposes. --- This visualization helps in understanding how the seismic waves spread from the epicenter to distant locales, reaching places as far as (-3, 2).
Title: Understanding the Outer Boundary of Earthquake Impact Question: Which equation represents the outer boundary of the area that could feel the earthquake? Options: a) \((x + 3)^2 + (y - 2)^2 = 52\) b) \((x - 1)^2 + (y + 4)^2 = 52\) c) \((x + 3)^2 + (y - 2)^2 = 100\) (Selected) d) \((x - 1)^2 + (y + 4)^2 = 100\) Explanation: This question is designed to test your understanding of coordinate geometry, particularly the equations of circles. Each option represents the equation of a circle in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is its radius. In this context, the correct equation will indicate the circle whose boundary defines the area affected by the earthquake. The center and radius of each circle can be identified as follows: a) Center: \((-3, 2)\), Radius: \(\sqrt{52}\) b) Center: \((1, -4)\), Radius: \(\sqrt{52}\) c) Center: \((-3, 2)\), Radius: \(10\) (Selected Equation) d) Center: \((1, -4)\), Radius: \(10\) By examining these options, we observe that option (c) \((x + 3)^2 + (y - 2)^2 = 100\) is selected as the correct equation. This equation describes a circle with a center at (-3, 2) and a radius of 10 units, which represents the furthest extent of the area that could feel the earthquake. Understanding how to interpret and work with equations of circles is crucial for various applications, including determining affected areas in natural disasters.
Transcribed Image Text:Title: Understanding the Outer Boundary of Earthquake Impact Question: Which equation represents the outer boundary of the area that could feel the earthquake? Options: a) \((x + 3)^2 + (y - 2)^2 = 52\) b) \((x - 1)^2 + (y + 4)^2 = 52\) c) \((x + 3)^2 + (y - 2)^2 = 100\) (Selected) d) \((x - 1)^2 + (y + 4)^2 = 100\) Explanation: This question is designed to test your understanding of coordinate geometry, particularly the equations of circles. Each option represents the equation of a circle in the standard form \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is its radius. In this context, the correct equation will indicate the circle whose boundary defines the area affected by the earthquake. The center and radius of each circle can be identified as follows: a) Center: \((-3, 2)\), Radius: \(\sqrt{52}\) b) Center: \((1, -4)\), Radius: \(\sqrt{52}\) c) Center: \((-3, 2)\), Radius: \(10\) (Selected Equation) d) Center: \((1, -4)\), Radius: \(10\) By examining these options, we observe that option (c) \((x + 3)^2 + (y - 2)^2 = 100\) is selected as the correct equation. This equation describes a circle with a center at (-3, 2) and a radius of 10 units, which represents the furthest extent of the area that could feel the earthquake. Understanding how to interpret and work with equations of circles is crucial for various applications, including determining affected areas in natural disasters.
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