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We are given five points plotted on a centimetre grid, which are five vertices of a regular hexagon. We are asked to determine the coordinates of the sixth vertex.

### Analysis:
1. A hexagon has six vertices, and each side of the hexagon has equal length.
2. By inspecting the grid:
   - The given points are:
     - (1, 5)
     - (3, 1)
     - (9, 1)
     - (11, 5)
     - (7, 9)
3. To form a regular hexagon, the missing vertex must be positioned such that the distances between adjacent vertices remain equal. Looking at the symmetry of the current points, it appears that the hexagon could be centrally symmetric.

### Step-by-Step Process:
- The center of symmetry appears to be around \((6, 5)\) since the points seem to be symmetrically distributed around this point.
- The missing vertex should maintain this symmetry. Based on the positions of the other points, one possible set of coordinates for the sixth vertex would be \((5, 9)\).

Thus, **one possible pair of coordinates for the missing vertex is (5, 9)**.

Would you like more details or have any other questions? 

Here are five related questions for deeper understanding:
1. How can we calculate the length of each side of the hexagon?
2. Why must the hexagon be symmetric in this problem?
3. How would the solution change if we altered the length of the hexagon's sides?
4. Can we calculate the center of the hexagon geometrically?
5. What are the properties of a regular hexagon that help solve this problem?

**Tip:** When solving geometric problems, symmetry is often a helpful property to exploit, especially with regular polygons like hexagons.

Five points are plotted on a centimetre grid. The five points are five vertices of a hexagon. Each side of the hexagon has the same length. Work out one possible pair of coordinates of the other vertex.

Learn how to find the missing vertex of a regular hexagon plotted on a grid. The problem involves analyzing symmetry and using the properties of regular polygons. Suitable for students in Grades 8-10.

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