Geometry

Question Analysis  

Determine the fourth vertex of a rectangle using coordinate - plane properties, specifically the relationships between opposite sides and right angles.

Key Concept Explanation  

In a rectangle, opposite sides are parallel and equal in length. The sides are perpendicular to each other (right angles). If two points  and  are on a horizontal line, ; if on a vertical line, .

Step - by - Step Solution  

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

For a rectangle, side  is parallel to side , and side  is parallel to side .

Since  is a vertical line (  for both

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