Given points , , , and , what kind of quadrilateral is ?

Question Analysis:
This question involves using coordinate - geometry concepts to identify the type of a quadrilateral.
The main focus is on calculating side lengths and slopes to determine the properties of the quadrilateral.

Key Concept Explanation:
A rectangle has opposite sides equal and parallel, and all angles are right angles (adjacent sides are perpendicular, meaning the product of their slopes is -1).
The distance formula

is used to find side lengths, and the slope formula

helps determine parallel and perpendicular relationships.

Step - by - Step Solution:
1. Calculate the lengths of the sides:
-

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