Geometry

Question Analysis

The core of this problem is leveraging coordinate - plane concepts to determine the fourth vertex of a rhombus. Key elements involve the properties of a rhombus, namely equal - length sides and the characteristic that its diagonals bisect each other at right angles.

Key Concept Explanation

Diagonal properties: The diagonals of a rhombus bisect one another. By using the mid - point formula , we can find the mid - point of a line segment between two points. If the mid - points of the two diagonals of a rhombus are the same, it helps in pinpointing the missing vertex.

Step - by - Step Solution

1. Identify the coordinates of the known points: Let , , .

2. Compute 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  must also be . Let the coordinates of

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