https://file.aiquickdraw.com/mathbot/file/1727105424239nnp83yq1.jpg

Let's analyze the polygon described by the given vertices:

The vertices of the polygon are at:
- (1, 1)
- (1, 8)
- (8, 1)
- (8, 8)

These points correspond to the corners of a rectangle or square on the coordinate plane. Let's confirm this:

- The distance between (1, 1) and (1, 8) is \( |8 - 1| = 7 \) units (a vertical side).
- The distance between (1, 1) and (8, 1) is \( |8 - 1| = 7 \) units (a horizontal side).

Since both sides are equal in length, and all angles formed by these points are 90°, this is a square. Therefore, the best description of this polygon is a **square**.

Would you like further details or have any questions?

### Related questions:
1. How do you calculate the area of this square?
2. How would the description change if one of the sides was not equal to 7 units?
3. What is the perimeter of this square?
4. How can you find the diagonal length of the square using the vertices?
5. What is the significance of the coordinates in determining the shape of a polygon?

### Tip:
When identifying polygons on a coordinate plane, use distance formulas and angle properties to verify the shape and type of polygon accurately.

Study the coordinate plane below. A certain polygon has its vertices at the following points: (1, 1), (1, 8), (8, 1), and (8, 8). What is the best description of this polygon?

Explore how to identify and describe a square on a coordinate plane using vertices. This page explains the properties of a square, how to use the distance and area formulas, and applies the Pythagorean theorem to verify square diagonals. Suitable for students in Grades 6-9.

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