Geometry

Question Analysis

The core of this problem is leveraging the mid - point property of parallelograms in the coordinate plane.

Key Concept Explanation

The mid - point formula for two points  and  is . For parallelogram , the mid - point of diagonal  will be the same as the mid - point of diagonal . 

Step - by - Step Solution

1. Determine the coordinates of the known points:

Let , , .

2. Calculate the mid - point of diagonal :

Using the mid - point formula .

3. Let the coordinates of  be

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