Geometry

Question Analysis

Determine the fourth vertex of a rhombus by leveraging properties of equal side lengths and diagonals bisecting each other in the coordinate plane.

Key Concept Explanation

Mid - point Formula: For two points  and , the mid - point  is . In a rhombus, diagonals bisect one another.

Step - by - Step Solution

1. Denote the known points: , , .

2. Calculate the mid - point of diagonal :

Using the mid - point formula, for  and , we have .

3. Since the diagonals of a rhombus bisect each other, the mid - point of diagonal

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