Geometry

Question Analysis

The main focus of this question is to determine the perimeter of a regular hexagon. It requires using the distance formula to find the length of one side based on the given endpoints, and then multiplying by the number of sides (6) since all sides of a regular hexagon are equal. This tests knowledge of regular polygon properties and coordinate - geometry skills.

 

Key Concept Explanation

Distance formula: For two points  and , the distance  between them is .

Regular polygon property: In a regular polygon, all side lengths are equal. The perimeter  of a regular polygon with  sides and side length  is .

 

Step - by - Step Solution

1. Calculate the length of one side:

Let  and .

Substitute into the distance formula:

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