A new game uses pieces shaped like the polygon in the graph where the scale is 1 unit equals 1 inch.

a. Determine whether the shape is a regular polygon.

Type your response in the space below.

To determine whether the shape is a regular polygon, we need to check two key properties:

1. **Equal side lengths**: All sides of a regular polygon must have the same length.
2. **Equal angles**: All interior angles of a regular polygon must be equal.

### Steps:

1. **Analyzing the Shape**:
   - The polygon is graphed on a coordinate plane with a scale where 1 unit equals 1 inch.
   - By looking at the graph, the polygon appears to be a quadrilateral (4-sided figure).
   
2. **Measuring Side Lengths**:
   - Using the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\), the distance is calculated as:
     \[
     d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
     \]
   - We can apply this formula to the four sides of the polygon using their coordinates from the graph.

3. **Checking Angle Equality**:
   - If the side lengths are all equal, we also need to check if the interior angles are equal to confirm the polygon is regular.

Without precise coordinates or angle measures, based on just the visual representation, the shape may not appear to be a regular polygon. However, verifying it using the distance formula and checking the angles would confirm this mathematically.

Would you like me to extract the coordinates from the graph and calculate the side lengths for you to proceed further?

Explore how to determine whether a polygon is regular using equal side lengths and angles. This problem involves analyzing polygon shapes on a coordinate plane with practical application of the distance formula and angle measurements. Suitable for students in Grades 9-12.

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