Geometry

Question Analysis

The problem requires using the properties of a parallelogram in the coordinate plane to find the fourth vertex. Key properties of a parallelogram include opposite sides being parallel and equal in length.

Key Concept Explanation

The mid - point formula between two points  and  is . For a parallelogram , the mid - point of diagonal  is the same as the mid - point of diagonal .

Step - by - Step Solution

1. First, find the coordinates of the known points: Let , , .

2. Using the mid - point property:

The diagonals of a parallelogram bisect each other. Let the mid - point of diagonal be the same as the mid - point of diagonal .

Calculate the mid - point of using the mid - point formula. For and , the mid - point

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