Geometry

Question Analysis  

Determine the fourth vertex of a square using the properties of equal side lengths and perpendicular sides in the coordinate plane.

Key Concept Explanation  

In a square, all sides are equal, and adjacent sides are perpendicular. Horizontally - aligned sides have the same  - coordinates for their endpoints, and vertically - aligned sides have the same  - coordinates for their endpoints.

Step - by - Step Solution  

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

The side  is a vertical line segment with length .

The side  is a horizontal line segment with length .

Since  is a square, the side opposite to

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