Geometry

Question Analysis

The main focus is to find the centroid of rectangle . We'll use the formula for the centroid of a polygon, which involves averaging the  - coordinates and  - coordinates of its vertices. Since it's a rectangle, the centroid is the intersection of its diagonals, and this formula helps us determine that point precisely.

 

Key Concept Explanation

For a polygon with  vertices having coordinates , , , , the coordinates of the centroid  are calculated as  and . In the case of a rectangle, we can also think of it as finding the mid - point of the diagonals.

 

Step - by - Step Solution

1. Identify the coordinates of the vertices:

Assume ,

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