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Let's go through the mathematical questions shown in the image step by step.

### 1. Consider the Voronoi diagram for sites A, B, C, D, and E.
**a. Identify the site(s) closest to:**
- i. (1, 0)
- ii. (-4, -2)
- iii. (3, -5)
- iv. (-3, 2)

To answer these, we'll need to look at which region each point lies in the Voronoi diagram. Each region corresponds to the points closest to a specific site.

**b. Are there any points that are equally closest to sites B and D?**
- Check if there are any boundary lines between the regions for B and D. Points on the boundary lines are equally close to both sites.

**c. Which point is equally closest to sites B, C, and E?**
- Look for an intersection of the boundaries of the Voronoi regions for B, C, and E. This would be the point equidistant from all three.

### 2. Let P be a point on an edge of a Voronoi cell.
Suppose a circle is drawn with center P, passing through X. Explain why this circle must pass through one other site.
- Since the circle is centered on the boundary of two cells, and passes through point X, it must pass through at least two sites because Voronoi edges are equidistant from their sites.

### 3. Construct a Voronoi diagram for the following sites:
- a. A(4, 7) and B(2, -1)
- b. A(-5, 0), B(1, 6), and C(7, 4)

You would sketch this diagram by plotting the points and constructing perpendicular bisectors between the pairs of sites to form regions.

### 4. This Voronoi diagram shows the taxi ranks in a city.
**a. Explain why the diagram must have a site missing.**
- If the diagram does not cover all areas, there may be a missing taxi rank (site).

**b. Find the coordinates of the missing site E.**
- The missing site would be located where its Voronoi cell should be. Look at the gaps in the diagram to estimate the location.

**c. Elizabeth is at (-3, 2), and needs to catch a taxi.**
- i. Which taxi rank is she closest to?
  - Check which Voronoi region (-3, 2) lies in.
- ii. Assuming she walks at 5 km/h, how long will it take her to walk to this taxi rank? What assumption are you making in your answer?
  - Calculate the distance from (-3, 2) to the nearest site and divide by her speed to get the time.

**d. Albert is at (-2, -2).**
- i. Which taxi rank is Albert closest to?
  - Determine which Voronoi cell (-2, -2) falls into.
- ii. What other factors might Albert consider when deciding which taxi rank to use?
  - He could consider factors like traffic, ease of access, or available taxis.

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If you'd like detailed help on any specific part of this review set, feel free to ask! Here are 5 related questions for deeper understanding:

1. How do you construct Voronoi diagrams for more than two sites?
2. Why do the Voronoi cells change shape based on the distribution of sites?
3. What is the significance of boundary lines in Voronoi diagrams?
4. How does the number of sites affect the complexity of a Voronoi diagram?
5. Can Voronoi diagrams be used in three dimensions?

**Tip:** Voronoi diagrams are useful in fields like meteorology, city planning, and network design, where the closest site or resource needs to be determined.

Voronoi diagram problems involving taxi ranks, site proximity, and missing coordinates.

Solve Voronoi diagram problems related to taxi ranks and site proximity. This set covers concepts like calculating equidistant points, identifying missing coordinates, and applying Voronoi diagrams to real-world scenarios. Suitable for high school students in Grades 10-12.

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