Geometry

Question Analysis  

Determine the fourth vertex of a rectangle using properties of parallel and perpendicular sides in the coordinate plane.

 

Key Concept Explanation  

Slope of a Line: The slope between two points and is calculated as . In a rectangle, opposite sides have equal slopes (are parallel), and the product of slopes of adjacent sides is - 1 (are perpendicular).

 

Step - by - Step Solution  

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

2. Calculate slopes:

The slope of is .

The slope of is . Since , and are perpendicular.

3. Find the fourth vertex using slope and parallel - side property:

Since is a rectangle, should be parallel to and should be parallel to .

The slope of the line parallel to (for side ) is . Let the coordinates of be . The slope between and is

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