Geometry

Question Analysis

The key is to use the properties of a square (perpendicular sides and equal side - lengths) in the coordinate plane to find the fourth vertex.

Key Concept Explanation

In a square, adjacent sides are perpendicular. Horizontal lines have the property that for any two points  and  on them, . Vertical lines have . The side - lengths of a square are equal.

Step - by - Step Solution

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

2. Analyze the side :

 is a horizontal line since the  - coordinates of  and  are the same (). The length of  is .

3. Analyze the side :

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