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14. OPEN RESPONSE Two ships follow the parallel paths shown on the map. O ty N 4x If 1 unit is 1 nautical mile, what is the shortest distance between the two paths? Round your answer to the nearest tenth. (Lesson 3-10

14. OPEN RESPONSE Two ships follow the parallel paths shown on the map. O ty N 4x If 1 unit is 1 nautical mile, what is the shortest distance between the two paths? Round your answer to the nearest tenth. (Lesson 3-10

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 shortest distance between the two paths? Round to nearest tenth?
### Open Response **Problem Statement:** Two ships follow the parallel paths shown on the map. **Diagram Analysis:** The diagram is a coordinate grid with two lines. These lines represent the paths of the ships. Each line is labeled with directional arrows and several points marked on the grid. The grid has scales along both the x-axis and y-axis, each marked from -4 to 4. The lines appear to be parallel, with one line passing through the origin (0,0). **Question:** If 1 unit is equivalent to 1 nautical mile, what is the shortest distance between the two paths? Round your answer to the nearest tenth. **Reference:** Lesson 3-10 from Module 3 Review on Logical Arguments and Line Relationships. **Solution Outline:** To find the shortest distance between two parallel lines on a coordinate plane, you can: 1. Determine the slope and y-intercepts of each line. 2. Use the distance formula for parallel lines: \[ d = \frac{|c_2 - c_1|}{\sqrt{1 + m^2}} \] where \( m \) is the slope, and \( c_1 \) and \( c_2 \) are the y-intercepts. 3. Substitute the values to calculate the distance in nautical miles. 4. Round the final answer to the nearest tenth.
Transcribed Image Text:### Open Response **Problem Statement:** Two ships follow the parallel paths shown on the map. **Diagram Analysis:** The diagram is a coordinate grid with two lines. These lines represent the paths of the ships. Each line is labeled with directional arrows and several points marked on the grid. The grid has scales along both the x-axis and y-axis, each marked from -4 to 4. The lines appear to be parallel, with one line passing through the origin (0,0). **Question:** If 1 unit is equivalent to 1 nautical mile, what is the shortest distance between the two paths? Round your answer to the nearest tenth. **Reference:** Lesson 3-10 from Module 3 Review on Logical Arguments and Line Relationships. **Solution Outline:** To find the shortest distance between two parallel lines on a coordinate plane, you can: 1. Determine the slope and y-intercepts of each line. 2. Use the distance formula for parallel lines: \[ d = \frac{|c_2 - c_1|}{\sqrt{1 + m^2}} \] where \( m \) is the slope, and \( c_1 \) and \( c_2 \) are the y-intercepts. 3. Substitute the values to calculate the distance in nautical miles. 4. Round the final answer to the nearest tenth.
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