Find the equation of the line which would complete the Voronoi cell containing site E. Give your answer in the form ax + by + d = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the equation of the line which would complete the Voronoi cell containing site E. Give your answer in the
form ax + by + d = 0.

This image features a coordinate plane graph with points marked at various locations. The graph is labeled with an x-axis and a y-axis. Below is a detailed description:

### Graph Description

**Axes:**
- The x-axis ranges from -4 to 16.
- The y-axis ranges from -4 to 12.

**Points:**
- **Point A** is located at (3, 1).
- **Point B** is located at (5, 7).
- **Point C** is located at (12, 8).
- **Point D** is located at (11, -1).
- **Point E** is located at (7, 5).

**Dashed Lines:**
- One dashed line runs diagonally from the top-left corner at (-4, 12) to the bottom-right corner at (16, -4). This line represents the equation \(y = -x + 12\).
- Another dashed line runs diagonally from the bottom-left corner at (-4, -4) to the top-right corner at (16, 16). This line represents the equation \(y = x\).

### Uses in Education
This graph can be used to teach students about the coordinate plane, the positioning of points, and the interpretation of linear equations. It is useful for lessons in geometry, algebra, and other areas of mathematics that involve graphing and spatial understanding. 

Students can practice plotting points, identifying the coordinates of given points, and understanding how different linear equations are represented on a graph.
Transcribed Image Text:This image features a coordinate plane graph with points marked at various locations. The graph is labeled with an x-axis and a y-axis. Below is a detailed description: ### Graph Description **Axes:** - The x-axis ranges from -4 to 16. - The y-axis ranges from -4 to 12. **Points:** - **Point A** is located at (3, 1). - **Point B** is located at (5, 7). - **Point C** is located at (12, 8). - **Point D** is located at (11, -1). - **Point E** is located at (7, 5). **Dashed Lines:** - One dashed line runs diagonally from the top-left corner at (-4, 12) to the bottom-right corner at (16, -4). This line represents the equation \(y = -x + 12\). - Another dashed line runs diagonally from the bottom-left corner at (-4, -4) to the top-right corner at (16, 16). This line represents the equation \(y = x\). ### Uses in Education This graph can be used to teach students about the coordinate plane, the positioning of points, and the interpretation of linear equations. It is useful for lessons in geometry, algebra, and other areas of mathematics that involve graphing and spatial understanding. Students can practice plotting points, identifying the coordinates of given points, and understanding how different linear equations are represented on a graph.
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