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The image you provided contains instructions on constructing Voronoi diagrams by hand using three points A(8, 14), B(16, 10), and C(8, 6). Here's a step-by-step breakdown of the process based on your image:

### Steps for Constructing Voronoi Diagrams:

1. **Find perpendicular bisectors**:
   - First, determine the line segments connecting each pair of points:
     - Line between A(8, 14) and B(16, 10)
     - Line between B(16, 10) and C(8, 6)
     - Line between C(8, 6) and A(8, 14)
   - For each of these lines, calculate the perpendicular bisector, which is the line perpendicular to the segment that passes through its midpoint.

2. **Draw each perpendicular bisector**:
   - Using graph paper, plot the perpendicular bisectors of the three lines from Step 1.

3. **Look for the intersection of the perpendicular bisectors**:
   - The intersection point of the bisectors defines the location where the regions (or cells) divide between the three sites (A, B, C).

4. **Remove excess perpendicular bisectors**:
   - Trim or remove the parts of the bisectors that do not separate the regions between the points, leaving each point (A, B, C) in its own distinct region.

### Steps to Solve:
- **Perpendicular bisector calculation**: For each pair of points, find the midpoint and the slope of the line segment connecting the points. The slope of the perpendicular bisector is the negative reciprocal of the original slope.
- **Plot bisectors on the graph** to accurately represent the Voronoi boundaries.

Would you like help calculating and drawing these bisectors step-by-step?

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### 5 Relative Questions:
1. How do you calculate the midpoint of a line segment between two points?
2. What is the formula for finding the slope between two points?
3. How do you find the equation of a line given a slope and a point?
4. How can you determine the perpendicular slope of a line?
5. How can Voronoi diagrams be used in practical applications, like geography or telecommunications?

### Tip:
When drawing perpendicular bisectors, always ensure that the lines are perfectly perpendicular by using the negative reciprocal of the original slope.

How to construct Voronoi Diagrams by hand using points A(8, 14), B(16, 10), and C(8, 6)?

Learn how to construct Voronoi diagrams by hand using points A(8, 14), B(16, 10), and C(8, 6). This step-by-step guide involves calculating perpendicular bisectors and finding intersections to divide the plane into regions for each point.

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